Finding the Roots of a Complex Number

Examples, solutions, videos, worksheets, games, and activities to help PreCalculus students learn how to find the roots of a complex number.

Finding the Roots of a Complex Number
We can use DeMoivre’s Theorem to calculate complex number roots. In many cases, these methods for calculating complex number roots can be useful, but for higher powers we should know the general four-step guide for calculating complex number roots. In order to use DeMoivre’s Theorem to find complex number roots we should have an understanding of the trigonometric form of complex numbers.

How to use DeMoivre’s Theorem to compute the cube roots of a complex number?

More Roots of Complex Numbers
We can use a simple four-step guide to help us find complex roots, or the nth roots of complex numbers. These guidelines simplify for us the process of using DeMoivre’s Theorem to find complex roots. This method for finding complex roots uses the trigonometric form and so we should understand how to convert from rectangular to trigonometric form and from trigonometric to rectangular form.

How to find the roots of a complex number quickly using four simple guidelines?

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Finding roots of complex numbers
This video gives the formula to find the n-th root of a complex number and use it to find the square roots of a number.

Finding roots of complex numbers, Ex 2
This video gives the formula to find the n-th root of a complex number and use it to find the square roots of a number. Note that the number must first be in polar form.

Finding roots of complex numbers, Ex 3
In this video, I find all of the cube roots of 64

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How to determine the nth roots of a complex number?

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