Math Playground
Numbers

Imaginary numbers

i is the square root of −1. Strange, but they make many problems easy.

i is the square root of −1. Imaginary numbers are multiples of i — like 2i, 5i, −7i.

Powers of i cycle

  • i¹ = i
  • i² = −1
  • i³ = −i
  • i⁴ = 1, then it repeats

They're called 'imaginary' for historical reasons — but they describe real things, like AC circuits and quantum waves.