Complex Number Calculator
A complex number has a real part and an imaginary part, written a + bi. On a flat graph it is a single point, and you can measure how far that point is from zero and what angle it sits at. This finds both.
- Free
- Works offline after your first visit
- Saves on this device
- No sign-up
- Updated
How it works
The size, or modulus, is the square root of a squared plus b squared. It is the straight-line distance from zero to the point.
The angle is worked out from the two parts with the arctangent of b over a, adjusted for which quarter of the graph the point is in. This calculator gives it in degrees, measured counterclockwise from the positive real axis.
Worked example
The number 3 + 4 i has a size of 5 and sits at an angle of 53.13 degrees.
Questions
What is the imaginary unit?
It is the square root of minus one, written i. The imaginary part is the number multiplying it.
Does this add or multiply complex numbers?
No. It only finds the size and angle of one number. Adding and multiplying need a different calculator.
Why can the angle be negative?
A negative imaginary part puts the point below the horizontal line, so the angle is measured the other way.
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