# 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

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

## Related Videos

Complex Logarithm