Multiply complex numbers
Type two complex numbers and get their product, with the real and imaginary part, the modulus and the argument.
Write as a + bi, for example 3 − 2i, −i or 4i.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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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 out the brackets and use i² = −1: (a + bi)(c + di) = (ac − bd) + (ad + bc)i. For (3 + 2i)(1 − 4i) = 3 − 12i + 2i − 8i² = 3 − 10i + 8 = 11 − 10i.
Geometric meaning
When you multiply, the moduli multiply and the arguments add up. Multiplying by i turns a number a quarter turn (90°) around the origin.
See also divide complex numbers.
Frequently asked questions
Is the multiply complex numbers free?
Yes. The multiply 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.