Complex Argument Calculator

This complex argument calculator works out the argument, or phase angle, of any complex number written as a plus bi, where a is the real part and b is the imaginary part. The argument is the angle the number makes with the positive real axis when plotted on the complex plane, and together with the modulus, or distance from the origin, it forms the polar form of a complex number. Working in polar form makes multiplying, dividing and raising complex numbers to powers far simpler than in rectangular form, which is why the argument shows up in electrical engineering, signal processing, control theory and maths courses alike. To use the tool, type the real part into the first field and the imaginary part into the second. It instantly returns the argument in degrees as the headline result, plus the same angle in radians and the modulus underneath, updating live as you change the numbers. Behind the scenes it uses the two-argument arctangent function, atan2, rather than a plain arctan, so the angle always lands in the correct quadrant, even when the real part is zero. The principal value returned sits between minus 180 and 180 degrees, or minus pi and pi radians. Results are rounded for display, so treat very small argument or modulus values near zero with a little care.

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