MihsabaHow to use
Complex numbers combine real and imaginary parts as a+bi. Choose an operation on z₁ and z₂; the tool reports the result, modulus, argument, conjugate and polar form.
- Choose add, subtract, multiply or divide.
- Enter real and imaginary parts for both numbers.
- Calculate.
- Review rectangular and polar forms, modulus and argument.
How it is calculated
(a+bi)(c+di)=(ac−bd)+(ad+bc)i; |z|=√(x²+y²)
Example
(3+4i)+(1−2i)=4+2i, whose modulus is √20≈4.472.
Important notes
Division by 0+0i is undefined. The argument is shown in degrees using atan2, normally from −180° to 180°.
Frequently asked questions
What is modulus?
|a+bi|=√(a²+b²).
What is the conjugate?
The conjugate of a+bi is a−bi.
What is polar form?
r∠θ, where r is modulus and θ is argument.
Is this calculator free?
Yes. It is free to use and requires no account.