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Created page with "<div style="font-size:30px">'''IMLOG (ComplexNumber,Base)'''</div><br/> *<math>ComplexNumber</math> is any complex number. *<math>Base</math> is the base value of the Log. ==..."
<div style="font-size:30px">'''IMLOG (ComplexNumber,Base)'''</div><br/>
*<math>ComplexNumber</math> is any complex number.
*<math>Base</math> is the base value of the Log.
==Description==
*This function shows the log value of a complex number.
*In <math>IMLOG (ComplexNumber,Base)</math>,<math>ComplexNumber</math> is any complex number.
*<math>Base</math> 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 <math>e^w = z</math>.
*The notation for such a <math>w</math> is <math>ln z</math> or <math>log z</math>.
*If <math>z = re^{iθ}</math> with <math>r > 0</math>which is in Polar form, then <math>w = ln r + iθ</math> is one logarithm of z.
*Adding integer multiples of 2πi gives all the others.
*The complex exponential function is not injective, because <math>e^{w+2\pi i} = e^w</math> for any w, since adding iθ to w has the effect of rotating <math>e^w</math> counterclockwise θ radians.
*So the points <math>.....w-4\pi i,w-2 \pi i, w, w+2\pi i,w+4 \pi i....</math>
*<math>ComplexNumber</math> is any complex number.
*<math>Base</math> is the base value of the Log.
==Description==
*This function shows the log value of a complex number.
*In <math>IMLOG (ComplexNumber,Base)</math>,<math>ComplexNumber</math> is any complex number.
*<math>Base</math> 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 <math>e^w = z</math>.
*The notation for such a <math>w</math> is <math>ln z</math> or <math>log z</math>.
*If <math>z = re^{iθ}</math> with <math>r > 0</math>which is in Polar form, then <math>w = ln r + iθ</math> is one logarithm of z.
*Adding integer multiples of 2πi gives all the others.
*The complex exponential function is not injective, because <math>e^{w+2\pi i} = e^w</math> for any w, since adding iθ to w has the effect of rotating <math>e^w</math> counterclockwise θ radians.
*So the points <math>.....w-4\pi i,w-2 \pi i, w, w+2\pi i,w+4 \pi i....</math>