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# Demoivre’s Theorem Calculator Online

The Demoivre’s Theorem Calculator is a powerful tool that simplifies complex number calculations. It allows users to raise a complex number to a given power efficiently and accurately. This calculator is particularly useful in various fields such as mathematics, physics, engineering, and signal processing.

### Formula of Demoivre’s Theorem Calculator

The formula used by the Demoivre’s Theorem Calculator is as follows:

z^n = r^n * (cos(n*theta) + i*sin(n*theta))

Where:

• z is the complex number.
• r is the magnitude (distance from the origin to the point in the complex plane).
• θ is the angle in radians between the positive x-axis and the line joining the origin to the point in the complex plane.
• n is the power to which the complex number is raise.

### General Terms Table

This table provides a quick reference for users to understand the terms commonly associated with complex numbers and the Demoivre’s Theorem.

### Example of Demoivre’s Theorem Calculator

Let’s illustrate the usage of the Demoivre’s Theorem Calculator with an example:

Suppose we have a complex number z = 3 + 4i, with a magnitude of r = 5 and an angle of θ = π/3 (60 degrees). If we want to raise this complex number to the power of n = 2, we can use the calculator to obtain the result.

### Most Common FAQs

Q: How do I use the Demoivre’s Theorem Calculator?

A: Simply input the complex number, its magnitude, angle in radians, and the desired power into the respective fields. Then, click the “Calculate” button to obtain the result.

Q: Can I use Demoivre’s Theorem for non-integer powers?

A: Yes, Demoivre’s Theorem can be extended to non-integer powers using the formula z^n = r^n * (cos(n*theta) + i*sin(n*theta)), allowing for fractional and negative exponents.