# Complex number n-th root calculator, step by step solution

This online calculator finds n-th root of the complex number with step by step solution. First thing you should do to find n-th root is to choose representation form (algebraic, trigonometric or exponential) of the initial complex number. Below we represent some minimal theoretical knowlegde to be able to understand step by step solution given by the calculator.

According the theory, n-th root of any number (n∈Z) has exactly n values. For example,

More interenting example:

where i - imaginary unit. As exercise, you can try to find third power of these values and make sure to get 8. There is a question: how to find all n root values from any given number? One should use the de Moivre's formula. So, complex number must be given in the trigonometric representation. Don't be worry, our online calculator automatically convert input data to trigonometric form as needed.