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SAT/Sphere
The all-in-one SAT prep platform for everyone!
© 2025 SAT/Sphere. All rights reserved.
SAT/Sphere
The all-in-one SAT prep platform for everyone!
© 2025 SAT/Sphere. All rights reserved.
Get 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.
Master the SAT with our targeted lesson on Complex Numbers, part of SAT Sphere’s Digital SAT curriculum. This lesson delivers in-depth concept explanations, problem-solving techniques, and SAT-style practice questions to help you improve your SAT performance. Ideal for both SAT Math and Reading & Writing, each lesson helps you build confidence for test day.
This SAT Sphere lesson focuses on essential SAT test topics in the Complex Numbers section. You'll build a strong understanding of core concepts, learn time-saving test-taking strategies, and apply your knowledge to realistic Digital SAT practice questions.
01
Introduction to Complex Numbers
Frames 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
Introduces 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
Defines 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
Teaches 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
Uses 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
Introduces complex conjugates and demonstrates division by rationalising denominators, refreshing rationalising-radicals techniques from Roots and Radicals.
07
Magnitude (Modulus) and Argument
Explains 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
Shows how to plot complex numbers as points and vectors in the complex plane, extending coordinate-geometry graphing skills.
09
Key Takeaways and Targeted Practice
Synthesises all complex-number operations into SAT-style mini-quiz problems that reinforce each learning objective.
View Example SAT Lesson with Practice Questions and Explanations
Each SAT Sphere lesson is a focused, interactive learning experience aligned with the new Digital SAT exam format. Lessons include SAT practice questions, detailed explanations, and concept reviews to support your SAT Math or Reading and Writing preparation. Designed for measurable improvement, our SAT lessons build confidence and mastery one topic at a time.
Engage with interactive SAT content featuring real-time practice and instant feedback.
Get personalized SAT prep tips and study guidance tailored to your strengths and weaknesses.
Access a complete Digital SAT curriculum that covers all tested topics and question types.
Build Your Digital SAT Skills with the Advanced Algebra and Functions Module
This lesson is part of the Advanced Algebra and Functions module, a structured SAT prep unit designed to improve your performance in key areas of the Digital SAT. Each module includes multiple SAT-focused lessons that develop critical thinking, analytical skills, and test-taking confidence. Progress through each module to strengthen your understanding and raise your overall SAT score.
Advance your SAT preparation by completing other SAT Sphere lessons in the Advanced Algebra and Functions module. Each lesson targets a specific concept tested on the Digital SAT, helping you deepen your knowledge and refine your skills for the real exam.
08
Modules
SAT Sphere includes 8 focused modules that cover every topic tested in the Math and Reading & Writing sections of the Digital SAT. Each module is built to strengthen core skills and test-taking ability.
86
Lessons
With 86 in-depth lessons, SAT Sphere helps you understand key SAT concepts clearly and efficiently. Our lessons break down each topic into simple, actionable parts.
10k+
Practice
Apply your knowledge using interactive SAT-style practice questions. Get immediate insights with feedback and explanations that help you improve fast.
+6k
Flash cards
Reinforce your learning with more than 6900 flash cards. Use them to review vocabulary, grammar, math facts, and more — anytime, anywhere.
Personalized study plan
Stay organized with our AI-powered study planner. Set your test date and daily study goals, and get a custom SAT prep plan tailored to your pace. Make consistent progress and be fully prepared by test day.
Find the perfect SAT prep plan designed to match your goals, study style, and budget. Begin your journey to top scores and college admission success with SAT Sphere!
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Ace the SAT Smarter, Not Harder
Confused by a question? Looking for a better way to understand the why, not just the what?
SAT/AI gives you personalized, step-by-step guidance that fits your learning style. Stuck on a tough math problem or confused by a reading passage? SAT/AI breaks it down clearly, offers instant feedback, and helps you learn from mistakes—building your confidence and boosting your score, one question at a time.
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Begin your SAT preparation with SAT Sphere's comprehensive Digital SAT course. Access expertly crafted SAT lessons, interactive practice questions, and proven strategies to improve your SAT Math and SAT Reading and Writing scores. Whether you're aiming for a perfect 1600 or looking to boost your score, SAT Sphere guides you step-by-step toward SAT success.
