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

Term | Description |
---|---|

Complex Number | A number that can be expressed in the form `a + bi` , where `a` and `b` are real numbers, and `i` is the imaginary unit. |

Magnitude | The distance from the origin to a point in the complex plane. |

Angle | The measure of rotation required to reach a point from the positive x-axis in radians. |

Power | The exponent to which the complex number is raised. |

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: What applications does Demoivre’s Theorem have?**

A: Demoivre’s Theorem is widely use in various fields such as electrical engineering, signal processing, and control theory for analyzing and manipulating complex numbers in polar form.

**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.