Math Playground
Algebra

Complex numbers

a + bi where i² = −1. The numbers that live off the real line.

Complex numbers extend reals with i, where i² = −1. Form: a + bi.

Operations

  • Add: (a+bi) + (c+di) = (a+c) + (b+d)i
  • Multiply: use FOIL, replace i² with −1.
  • Conjugate: of a+bi is a−bi.
Try it

(2 + 3i)(1 − i)

2 − 2i + 3i − 3i² = 2 + i + 3 = 5 + i.