Complex Numbers
Add, multiply and divide complex numbers, and find the modulus, conjugate and polar form, with i² = −1 applied at each step. Try “(3 + 4i)(2 − i)”.
Try an example:
What you can do with the Complex Numbers
Add, multiply, divide, modulus, conjugate and polar form.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. (3 + 4i)(2 - i)
How the Complex Numbers works
- Expand like brackets, treating i as a variable.
- Replace i² with −1 and collect the real and imaginary parts.
- For division, multiply top and bottom by the conjugate of the denominator.
Frequently asked questions
What is the modulus of a complex number?
For a + bi it is √(a² + b²), the distance from the origin on the complex plane.
What is a complex conjugate?
The conjugate of a + bi is a − bi. A number times its conjugate is always real.
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