## Logarithm of a Complex Number

Suppose is a complex number. We can perform natural logarithm of the complex number is a complex number. We can perform natural logarithm of the complex number

Since is only determined only up to multiple of 2PI, the complex natural logarithm has infinitely many values.

## Properties of Complex Logarithm

If and are complex numbers then

- Addition of logarithm:
- Subtraction of logarithm:
- General Power:
- Root:

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

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