Complex Number Calculator
Enter two complex numbers and choose an operation. The Argand diagram shows both inputs and the result as vectors. Step-by-step KaTeX shows every calculation.
Input
z1 = a + bi
z2 = c + di
Results
Result (rectangular)
4 + 2i
Modulus |z|
4.472136
Argument (radians)
0.463648
Argument (degrees)
26.57°
Polar form
4.4721 ∠ 26.57°
Argand Diagram
Step-by-Step
1. Formula
2. Substitute
3. Result
Reference Guide
Addition and Subtraction
Add or subtract the real and imaginary parts separately.
Multiplication
Use FOIL and remember that i squared equals -1.
Division
Multiply numerator and denominator by the conjugate of the denominator to eliminate i from the bottom.
Polar Form
Every complex number can be written in polar form using its modulus and argument.
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