### Math

# Complex Number Power Formula with Problem Solution & Solved Example

**Complex Number Power Formula**

Either you are adding, subtracting, multiplying, dividing or taking the root or power of complex numbers then there are always multiple methods to solve the problem using polar or rectangular method.

Based on research and practice, this is clear that polar form always provides a much faster solution for complex number powers than rectangular form. Power of complex numbers is a special case of products when the power is a whole positive number.

To understand the concept in deep, recall the nth root of unity first or this is just another name for nth root of one. The fourth root of complex numbers would be ±1, ±I, similar to the case of absolute values. If we will find the 8^{th} root of unity then values will be different again.

Now take the example of the sixth root of unity that moves around the circle at 60-degree intervals. For the triangle with vertices 0 and 1 then the triangle is called the equilateral triangle and it helps in determining the coordinates of triangles quickly.

**Complex Number Power Formula**

\[\LARGE z^{n}=(re^{i\theta})^{n}=r^{n}e^{in\theta}\]

Once you working on complex numbers, you should understand about real roots and imaginary roots too. They are usually given in both plus-minus order and can be used as per the requirement.

The other name related to complex numbers is primitive roots and this is fun to learn complex number power formula and roots. In beginning, the concepts may sound tough but a little practice always makes things easier for you.