# Manuals/calci/IMLOG

**IMLOG (ComplexNumber,Base)**

- is any complex number of the form x+iy.
- is the base value of the Log.
- IMLOG(),returns the logarithm of a complex number to the given base.

## Description

- This function shows the log value of a complex number.
- In , is any complex number.
- is the base value of a Log values.
- A complex logarithm function is an "inverse" of the complex exponential function.
- It is same as the real natural logarithm ln x is the inverse of the real exponential function.
- Thus, a logarithm of a complex number z is a complex number w such that .
- The notation for such a is or .
- If with which is in Polar form, then is one logarithm of z.
- Adding integer multiples of 2πi gives all the others.
- The complex exponential function is not injective, because for any w, since adding iθ to w has the effect of rotating counterclockwise θ radians.
- So the points

## Examples

- IMLOG("2+3i",2) = 1.850219859070546+ⅈ1.417871630745722
- IMLOG("9-5i",3) = 2.122422597222964-ⅈ0.4615809504617068
- IMLOG("9-5i",6) = 1.3013574573492332-ⅈ0.2830170640096076
- IMLOG("54",5) =2.4784951415313494+ⅈ0
- IMLOG("-19i",9) = 1.3400719296231876-ⅈ0.7149002168450317