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