Complex Numbers
Treat i like a variable, but replace i² with −1.
The rules
- i² = −1, i³ = −i, i⁴ = 1, and the cycle repeats every four powers.
- Add and subtract the real and imaginary parts separately.
- Multiply with FOIL, then replace i² with −1.
- To divide, multiply the top and bottom by the conjugate of the denominator.
Watch out: Forgetting that i² becomes −1, so the sign flips.
Worked example
What is (2 + 3i)(1 − i)?
- FOIL: 2 − 2i + 3i − 3i².
- Replace i² with −1: 2 + i + 3 = 5 + i.
Answer: 5 + i
Try it yourself
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