Complex Number Calculator

Add, subtract, multiply and divide complex numbers, then find real and imaginary parts, magnitude, conjugate and polar form.

Calculate with complex numbers in a + bi form

Enter complex numbers in a+bi form to perform arithmetic or inspect a single number.

The calculator separates real and imaginary parts and can return magnitude, conjugate and polar form.

Learn the concept

Try these examples

  • (2+3i) + (1-4i)
  • (2+3i) - (1-4i)
  • (2+3i)(1-4i)

Quick reference

  • (a+bi)(c+di) = (ac−bd) + (ad+bc)i.
  • |a+bi| = √(a²+b²).
  • Conjugate of a+bi is a−bi.

FAQ

How should I enter a complex number?

Use a+bi form, such as 2+3i, -4i or 5.

Can I divide complex numbers?

Yes. The calculator multiplies by the conjugate of the denominator and rejects division by 0+0i.

Sources and review

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