Aula de preparação para o SAT: Complex Numbers
🇺🇸 In EnglishGet comfortable with imaginary units and perform complex arithmetic step by step. Practice SAT-style drills to reinforce each operation. Tackle any complex-number problem with ease.
Domine o SAT com nossa aula focada em Complex Numbers, parte do currículo Digital SAT da SAT Sphere. Esta aula fornece explicações detalhadas de conceitos, técnicas de resolução de problemas e questões práticas no estilo SAT para ajudar você a melhorar seu desempenho. Ideal para Matemática SAT e Leitura & Escrita, cada aula ajuda a construir confiança para o dia do exame.
Tópicos SAT cobertos na aula Complex Numbers
Esta aula da SAT Sphere foca nos tópicos essenciais do exame SAT na seção Complex Numbers. Você desenvolverá uma compreensão sólida dos conceitos principais, aprenderá estratégias para economizar tempo no teste e aplicará seus conhecimentos em questões práticas realistas do Digital SAT.
01
Introduction to Complex Numbers
🇺🇸 In EnglishFrames the lesson goals for complex numbers on the Digital SAT and reminds students of required prior skills: laws of exponents, simplifying square roots, and plotting points on a coordinate plane.
02
The Imaginary Unit and Its Powers
🇺🇸 In EnglishIntroduces the imaginary unit i (√−1) and explores its cyclic powers, building on exponent rules from the earlier Introduction to Exponents and Powers lesson.
03
Standard Form and Equality of Complex Numbers
🇺🇸 In EnglishDefines complex numbers in a + bi form and shows how to test equality by matching real and imaginary parts, refreshing combining-like-terms skills from Simplifying Algebraic Expressions.
04
Addition and Subtraction of Complex Numbers
🇺🇸 In EnglishTeaches how to add and subtract complex numbers by separately combining real and imaginary parts, extending previous practice with combining like terms.
05
Multiplication of Complex Numbers
🇺🇸 In EnglishUses the distributive property and FOIL to multiply complex numbers while applying i² = −1, building on the earlier Multiplication of Expressions lesson.
06
Complex Conjugates and Division
🇺🇸 In EnglishIntroduces complex conjugates and demonstrates division by rationalising denominators, refreshing rationalising-radicals techniques from Roots and Radicals.
07
Magnitude (Modulus) and Argument
🇺🇸 In EnglishExplains how to calculate the modulus and argument of a complex number, connecting to the Pythagorean theorem from Properties of Triangles and inverse-trigonometric ideas.
08
Graphing Complex Numbers on the Complex Plane
🇺🇸 In EnglishShows how to plot complex numbers as points and vectors in the complex plane, extending coordinate-geometry graphing skills.
09
Key Takeaways and Targeted Practice
🇺🇸 In EnglishSynthesises all complex-number operations into SAT-style mini-quiz problems that reinforce each learning objective.
Ver lição de exemplo do SAT com questões e explicações
Cada aula da SAT Sphere é uma experiência de aprendizado interativa e focada, alinhada ao novo formato do Digital SAT. As aulas incluem questões práticas SAT, explicações detalhadas e revisões de conceitos para apoiar sua preparação em Matemática ou Leitura & Escrita. Projetadas para melhoria mensurável, nossas aulas de SAT constroem confiança e domínio, tópico por tópico.
Interaja com conteúdo SAT interativo com prática em tempo real e feedback instantâneo.
Receba dicas de preparação SAT personalizada e orientação de estudo adaptadas aos seus pontos fortes e fracos.
Acesse um currículo completo de Digital SAT que cobre todos os tópicos e tipos de questões testados.
Desenvolva suas habilidades no Digital SAT com o módulo Advanced Algebra and Functions
Esta aula faz parte do módulo Advanced Algebra and Functions, uma unidade estruturada de preparação SAT projetada para melhorar seu desempenho em áreas-chave do Digital SAT. Cada módulo inclui várias aulas focadas em SAT que desenvolvem pensamento crítico, habilidades analíticas e confiança para o exame. Avance por cada módulo para fortalecer sua compreensão e aumentar sua pontuação total no SAT.
Explore mais aulas Digital SAT no módulo Advanced Algebra and Functions
Aperfeiçoe sua preparação para o SAT concluindo outras aulas da SAT Sphere no módulo Advanced Algebra and Functions. Cada aula aborda um conceito específico testado no Digital SAT, ajudando você a aprofundar seus conhecimentos e aprimorar suas habilidades para o exame real.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
Word Problems and Applications
Translating word problems into algebraic expressions and equations. Solving practical problems using algebra.
Rational Expressions
Simplifying rational expressions. Solving equations involving rational expressions.
Functions and Their Graphs
Understanding the concept of functions. Graphing linear, quadratic, and exponential functions.
Polynomial Functions
Understanding polynomial expressions and their properties. Addition, subtraction, multiplication, and division of polynomials.
Sequences and Series
Understanding arithmetic and geometric sequences. Summation of series.
Quadratic Equations
Introduction to quadratic equations and their properties. Solving quadratic equations by factoring, completing the square, and the quadratic formula.
Systems of Equations
Methods for solving systems of linear equations (substitution, elimination). Application in real-world scenarios.
Exponential Functions
Understanding exponential growth and decay. Solving exponential equations.
Radical Expressions and Equations
Simplifying radical expressions. Solving equations involving radicals.
Logarithmic Functions
Introduction to logarithms and their properties. Solving logarithmic equations and applications.
O nosso Curso Digital SAT
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Módulos
A SAT Sphere oferece 8 módulos concebidos por especialistas, cobrindo Matemática e Leitura & Redação. Cada módulo foca tópicos essenciais do SAT, garantindo uma preparação completa.
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Lições
Com 86 lições detalhadas, a SAT Sphere cobre todos os aspetos do Exame Digital SAT. Cada lição decompoõe conceitos complexos em partes fáceis de digerir, tornando a aprendizagem eficaz e envolvente.
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