Calxsolver
Precalculus

Complex Number Calculator

A complex number has a real part and an imaginary part, written a + bi. This calculator adds, subtracts, multiplies and divides two complex numbers, showing the FOIL expansion or conjugate trick, and reports the modulus of the result.

Complex Number Calculator

Add, subtract, multiply or divide complex numbers.

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Frequently asked questions

How do you multiply complex numbers?

Use FOIL and the rule i² = −1: (a + bi)(c + di) = (ac − bd) + (ad + bc)i.

How do you divide complex numbers?

Multiply the numerator and denominator by the conjugate of the denominator, which makes the denominator the real number c² + d².

What is the modulus of a complex number?

The modulus |z| is its distance from the origin, √(real² + imaginary²).

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