Manuals/calci/IMLOG

IMLOG (ComplexNumber,Base)

• $ComplexNumber$ is any complex number of the form x+iy.
• $Base$ 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 $IMLOG(ComplexNumber,Base)$,$ComplexNumber$ is any complex number.
• $Base$ 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 $e^{w}=z$.
• The notation for such a $w$ is $lnz$ or $logz$.
• If $z=re^{i\theta }$ with $r>0$which is in Polar form, then $w=lnr+i\theta$ is one logarithm of z.
• Adding integer multiples of 2πi gives all the others.
• The complex exponential function is not injective, because $e^{w+2\pi i}=e^{w}$ for any w, since adding iθ to w has the effect of rotating $e^{w}$ counterclockwise θ radians.
• So the points $.....w-4\pi i,w-2\pi i,w,w+2\pi i,w+4\pi i....$

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

See Also

• LOG
• LOGINV
• ANTILOG

References

• Complex Log

• List of Main Z Functions

• Z3 home