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Year 11 · Counting & Number
Multiply complex numbers
A complex number has a real part and an imaginary part: a + bi, where i² = −1.
How to do it
- Add or subtract: combine real parts and imaginary parts separately.
- Multiply: expand like brackets and replace i² with −1.
- Modulus: √(a² + b²). Argument: the angle from the positive real axis.
Worked example
Simplify: (-2-2i)(-3-3i)
Expand like brackets and use i² = −1: (-2)(-3) + (-2)(-3)i + (-2)(-3)i + (-2)(-3)i² = 6 + 12i − 6 = 12i.
Answer: 12i
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Watch outi² is −1, not 1.
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