How to Calculate Complex Numbers
What is Complex Numbers?
A complex number z = a + bi combines real part a and imaginary part b, where i = √(−1). Complex numbers extend the real line to a 2D plane and are essential in engineering, physics, and signal processing.
Step-by-Step Guide
- 1Addition: (a+bi)+(c+di) = (a+c)+(b+d)i
- 2Multiplication: (a+bi)(c+di) = (ac−bd)+(ad+bc)i
- 3Magnitude |z| = √(a²+b²) · Argument θ = atan2(b,a)
Worked Examples
Input
(3+4i) × (1−2i)
Result
11−2i · |z|=√125
(3+8)+(4-6)i=11-2i
Ready to calculate? Try the free Complex Numbers Calculator
Try it yourself →