Add complex numbers
Type two complex numbers, such as 3 + 2i and 1 − 4i, and get their sum, 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
Add the real parts and the imaginary parts separately: (3 + 2i) + (1 − 4i) = (3 + 1) + (2 − 4)i = 4 − 2i. On the complex plane, that is adding two arrows head to tail.
Modulus and argument
The modulus |z| is the distance to the origin, √(a² + b²), and the argument is the angle with the positive real axis. For 4 − 2i: |z| ≈ 4.472 and the argument ≈ −26.57°.
Write numbers as a + bi, such as 3 − 2i, −i or 4i. See also subtract, multiply and divide complex numbers.
Frequently asked questions
Is the add complex numbers free?
Yes. The add 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.