Complex Numbers Basics

Front

Complex number

Back

a + bi

Front

Real part

Back

a in a + bi

Front

Imaginary part

Back

b in a + bi

Front

Imaginary unit

Back

i, where i² = -1

Front

Addition

Back

(a+bi) + (c+di) = (a+c) + (b+d)i

Front

Subtraction

Back

(a+bi) - (c+di) = (a-c) + (b-d)i

Front

Multiplication

Back

(a+bi)(c+di) = ac + adi + bci + bdi²

Front

Conjugate

Back

a - bi

Front

Modulus

Back

|a + bi| = √(a² + b²)

Front

Polar form

Back

r(cos θ + i sin θ)