Divide complex numbers
Type two complex numbers and get the quotient, with the real and imaginary part, the modulus and the argument.
Write as a + bi, for example 3 − 2i, −i or 4i.
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How it's worked out
How it works
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Instant answer
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How it works
Multiply the numerator and the denominator by the complex conjugate of the denominator (change the sign of its imaginary part). The denominator then becomes a real number:
(3 + 2i) / (1 − 4i) = (3 + 2i)(1 + 4i) / ((1 − 4i)(1 + 4i)) = (−5 + 14i) / 17 ≈ −0.294 + 0.824i.
When dividing, the moduli divide and the arguments subtract. Dividing by 0 is not possible. See also multiply complex numbers.
Frequently asked questions
Is the divide complex numbers free?
Yes. The divide complex numbers is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.