Read the result
The modulus is a length, so it is never negative. The argument is the direction of the complex number from the positive real axis.
Complex numbers
Complex Polar Converter
Convert a + bi into modulus-argument form without losing the quadrant information.
Formula
r = sqrt(a^2 + b^2), theta = atan2(b, a)
Result
Worked substitution
Polar form records a complex number by distance from the origin and angle from the positive real axis.
Where it helps
Polar form is the natural setup for powers, roots, rotations, phasors, and multiplication by a complex factor.
Common slip
The zero complex number has modulus 0 but no single direction. Treat its argument as undefined, not 0 by default.
Try it
Convert -1 + i and compare the angle with the diagram. It should sit in quadrant II.