Complex arithmetic
Add, subtract, multiply (with i² = −1), divide by multiplying numerator and denominator by conjugate.
Treat i like a variable, then replace i² with −1. Division: multiply top and bottom by the conjugate of the denominator to make it real.
Worked examples
(2 + 3i) + (1 − i) = 3 + 2i.
(2 + 3i)(1 − i) = 2 − 2i + 3i − 3i² = 5 + i.
(1 + 2i)/(3 − i) = (1+2i)(3+i) / ((3-i)(3+i)) = (1 + 7i)/10.
Frequently asked questions
Why multiply by conjugate when dividing?
It rationalises the denominator (makes it real).
Order of operations?
Same as ordinary algebra. i squared = −1.