Complex numbers z = a+bi where i²=−1. Addition: (a+bi)+(c+di) = (a+c)+(b+d)i. Multiplication: (a+bi)(c+di) = (ac−bd)+(ad+bc)i. Modulus: |z| = √(a²+b²). Argument: arg(z) = atan2(b,a). Polar: z = r·e^(iθ) = r(cosθ+isinθ).
How to Use
Enter two complex numbers:
- Real part (a): Coefficient of 1
- Imaginary part (b): Coefficient of i
- Operation: +, −, ×, ÷
Polar Form
- r = |z| = √(a²+b²)
- θ = arg(z) = atan2(b,a)
- z = r(cosθ + isinθ)
Complex Division
Multiply top and bottom by conjugate of denominator: (a+bi)/(c+di) = (a+bi)(c−di)/(c²+d²).
Step-by-Step Instructions
- 1Enter z₁ = a + bi.
- 2Enter z₂ = c + di.
- 3Select operation.
- 4View result.
- 5Check modulus and polar form.