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Year 11 · Counting & Number
Add and subtract 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: (6-3i) + (-2-3i)
Add the real parts (6 + -2 = 4) and the imaginary parts (-3 + -3 = -6): 4-6i.
Answer: 4-6i
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Watch outi² is −1, not 1.
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