Meet i — adding & multiplying
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Question
What is i?
Answer
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.
Question
How do you add or subtract complex numbers?
Answer
Combine the real parts together and the imaginary parts together — they don't mix.
Question
How do you multiply complex numbers?
Answer
Expand like two brackets (FOIL), then replace every i² with −1 and collect terms.
Question
(3 + 2i) + (1 − 5i) = ?
Answer
4 − 3i.
Question
(3 + 2i)(1 − 4i) = ?
Answer
3 − 12i + 2i − 8i² = 3 − 10i + 8 = 11 − 10i.
Question
Powers of i: i, i², i³, i⁴?
Answer
i, −1, −i, 1 — then the cycle repeats.
Question
What does i² equal, and why does it matter?
Answer
i² = −1; it's the step that turns a multiplication of complex numbers back into a + bi form.
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Full study notes for Meet i — adding & multiplying
Topic 1.12 hub
Complex numbers: Cartesian (HL only)
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