Suppose is a complex number. We can perform exponent of the complex number

## Properties of Complex Exponent

- Multiplication of exponent , if and are complex numbers.
- When the two complex numbers are negative to each other,
- Euler formula is obtained from complex exponent of pure imaginary component with absolute value 1, that is such that
- Since and , using Euler formula we can get .
- Since and , using Euler formula we can get
- Since and , using Euler formula we can get and .
- Complex exponent is periodic with the imaginary period , .

**
See Also
**
:
Complex Power
,
Complex Root
,
Complex Logarithm

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