Imaginary Unit (i)

★★★☆☆High School

📖Definition

i is the imaginary unit satisfying i² = -1. It's fundamental to complex numbers and essential in math and engineering.

i = √-1, i² = -1

Definition of imaginary unit

i⁰ = 1, i¹ = i, i² = -1, i³ = -i, i⁴ = 1

Powers of i cycle

z = a + bi

General form of complex number

예제 1

Calculate i^100.

예제 2

Calculate (2 + 3i)(1 - i).

Discovered by: Gerolamo Cardano (1545)

Introduced while solving cubic equations; Euler and Gauss systematized it.

AC circuits, impedance

Wave functions

Fourier transform

#허수#복소수#imaginary#complex