How to Use Complex Roots Calculator
The Complex Roots Calculator finds every nth root of a complex number. Choose expression, parts, or polar input mode, enter the complex number, and set n. The Complex Roots Calculator returns all roots as a + bi values.
Each result also includes modulus and argument information. This makes the Complex Roots Calculator useful for checking both rectangular and polar forms.
Formula & Theory — Complex Roots Calculator
The Complex Roots Calculator uses z = r(cos theta + i sin theta). The nth roots are zk = r^(1/n)[cos((theta + 2pi k)/n) + i sin((theta + 2pi k)/n)], where k = 0, 1, ..., n - 1.
The roots are evenly spaced around a circle in the complex plane. The Complex Roots Calculator computes each angle and converts the answer back to algebraic form.
Use Cases for Complex Roots Calculator
Use the Complex Roots Calculator for complex arithmetic, algebra, engineering mathematics, signal processing, phasor work, and polynomial root practice. The Complex Roots Calculator is especially helpful when several roots must be listed accurately.