i² = −1

↳definition of the imaginary unit

z = a + bi

↳3 + 4i has Re=3, Im=4

|z| = √(a² + b²)

↳|3+4i| = √(9+16) = 5

Conjugate: z̄ = a − bi

↳5 − 2i → conjugate is 5 + 2i

Multiply: (a+bi)(c+di) = (ac−bd) + (ad+bc)i

↳(1+i)(1−i) = 1 − i² = 2

Euler: e^(iθ) = cos θ + i sin θ

↳e^(iπ) = −1; e^(iπ) + 1 = 0