This De Moivre’s Theorem calculator tool will help you efficiently compute powers and roots of complex numbers.

## De Moivre’s Theorem Calculator

### How to Use the Calculator

To use the calculator, enter a complex number in the form of `a+bi`

where `a`

and `b`

are real numbers. `b`

must include the sign (+ or -) before it. Next, enter the power `n`

, which is an integer, for the exponentiation. Then click the “Calculate” button and the result will be displayed in the Result field.

### How It Calculates the Results

De Moivre’s Theorem states that any complex number `a+bi`

raised to the power `n`

can be expressed as `r^n(cos(nθ) + isin(nθ))`

, where `r`

is the modulus of the complex number and `θ`

is the argument. This calculator first converts your input into polar coordinates, calculates the new modulus and argument for the given power, and then converts this back to rectangular coordinates to provide the result.

### Limitations

The calculator currently requires that the input strictly follows the format `a+bi`

with no additional spaces and `i`

must be in lowercase. It does not support expressions in polar form directly and cannot handle symbols or letters other than `i`

. The power `n`

has to be an integer and not a fraction or a decimal. Results are rounded to two decimal places, larger powers may result in lower precision due to limitations in floating-point representation in JavaScript.