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Complex number calculator
Add, multiply, divide and find the modulus, angle and powers of complex numbers.
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About Complex number calculator
Work with numbers of the form a + bi: add, subtract, multiply, divide, and get the modulus, angle and powers. The modulus is the square root of a squared plus b squared. Handy for electrical engineering phasors, algebra homework and checking polar form results by hand.
How to use Complex number calculator
- Enter the real and imaginary parts of the first complex number.
- Choose an operation such as add, multiply, divide or power, and enter the second number if needed.
- Read the result along with its modulus and angle.
Why use this tool?
- Private: everything happens in your browser. Nothing you enter is uploaded.
- Free, with no sign-up, no watermark and no limit on how often you use it.
- Works on phones, tablets and computers: Android, iPhone, Windows, Mac and Linux. Nothing to install.
- Free to embed on your own website, with a ready-made code to copy.
- Available in 10 languages.
Also known as
Frequently asked questions
How do I write a complex number in polar form?
Find the modulus r = sqrt(a squared + b squared) and the angle theta with atan2(b, a). The number is then r(cos theta + i sin theta), often shortened to r angle theta.
How do I divide complex numbers by hand?
Multiply the top and bottom by the conjugate of the denominator. The denominator becomes a real number, a squared plus b squared, and you can split the result into real and imaginary parts.
What is the modulus of a complex number?
The modulus is its distance from zero on the complex plane, the square root of the real part squared plus the imaginary part squared. It is also called the absolute value or magnitude.
Is Complex number calculator free?
Yes. Complex number calculator on Toolipedia is free to use, with no sign-up and no watermark.
Is it safe to use?
Yes. Everything is worked out in your browser, and nothing you enter is sent to our server.
Does it work on my phone?
Yes. It works in any modern browser on Android and iPhone, as well as on tablets and computers. There's nothing to install.
Do I need an account?
No. Just open the page and use the tool. There's no sign-up and no email needed.
Can I put Complex number calculator on my own website?
Yes. Use the Embed on your site button under the tool to copy a short piece of code and paste it into your page. It is free, needs no account, and the tool keeps working inside your page.