Complex numbers in Cartesian form
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Flip to reveal answersWhat is i, and what is i²?
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All 8 Flashcards — Complex numbers in Cartesian form
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Question
What is i, and what is i²?
Answer
i is the imaginary unit, defined by i² = −1 (so i = √−1).
Question
What is the Cartesian form of a complex number?
Answer
z = a + bi, where a is the real part and b is the imaginary part (both real numbers).
Question
How do you add or subtract complex numbers?
Answer
Combine the real parts together and the imaginary parts together (treat i like a letter).
Question
How do you multiply complex numbers?
Answer
Expand the brackets, then replace every i² with −1 and collect like terms.
Question
What is the conjugate of z = a + bi, and why is it useful?
Answer
z* = a − bi (flip the sign of the imaginary part). z·z* = a² + b² is real, which lets you divide.
Question
How do you divide complex numbers?
Answer
Multiply top and bottom by the conjugate of the denominator, making the bottom real, then split into a + bi.
Question
What does an Argand diagram show, and where is z = a + bi plotted?
Answer
It plots complex numbers; z = a + bi is the point (a, b) — real across, imaginary up.
Question
What is the modulus |z| of z = a + bi?
Answer
|z| = √(a² + b²), the distance from the origin to (a, b) on the Argand diagram.
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Full study notes for Complex numbers in Cartesian form
Topic 1.12 hub
Complex numbers: intro (HL only)
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