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# Taking the natural log of a negative number is Excel.3

## Taking the natural log of a negative number is Excel.

(OP)
Is there a way to calculate the natural log of a negative number (It should yield two solutions) in Excel without getting an error message.  Your help is greatly appreciated.

pmans
Replies continue below

### RE: Taking the natural log of a negative number is Excel.

I believe ln(x) where x is negative gives complex results; you might try looking up the excel functions that deal with complex numbers.

### RE: Taking the natural log of a negative number is Excel.

Install the Analysis Toolpak with the Tools|Add-Ins command.  Then use function IMLN(number).

### RE: Taking the natural log of a negative number is Excel.

(OP)
jghrist,

The IMLN(number) function works, but yields a "text" cell.  Do you know how to change this into a "number" cell, so it can be used as part of an equation somewhere else in the spreadsheet.

pmans

### RE: Taking the natural log of a negative number is Excel.

imln returns a complex number.  That complex number can be manipulated with other im- functions (improduct, imsum, imreal etc).

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### RE: Taking the natural log of a negative number is Excel.

... but if you try to use normal floating point arithmetic functions (+, -,/,*,cos etc) on a complex number, it won't work.

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### RE: Taking the natural log of a negative number is Excel.

The text cell represents both parts of the imaginary number.  You'll have to parse out the real and imaginary parts separately into two different cells, using something like the MID and FIND functions to figure out where each part starts and stops.

### RE: Taking the natural log of a negative number is Excel.

IMREAL(complex number) will give the number value of the real part and IMAGINARY(complex number) will give the imaginary part.

Doing complex math with the analysis toolpack is a pain in the a**.  If you do a lot, get something like MathCAD.

### RE: Taking the natural log of a negative number is Excel.

(OP)
Thanks electricpete, BML, and jghrist for all your help. I got what I wanted, by using the IMREAL and the IMAGINARY functions.

Here is a follow-up question, related to the imaginary part of the solution.  I've noticed that the imaginary part of the natural log of any negative number is 3.14..i or PIi.  Do you guys know why that is?  What's the significance of PI in the imaginary part of the solution?

pmans

### RE: Taking the natural log of a negative number is Excel.

It comes from what I recall is called Euler's Theorem
e^(i*Pi) = -1
from which it follows that
log(-1) = i*Pi

Then from basic (non-complex) maths we have
log[(-1)*(x)] = log(-1) + log(x)

QED

### RE: Taking the natural log of a negative number is Excel.

Denial nailed it.

bml and jgrhist - it sounds like  you are saying the only thing we can do with a complex result is parse it into real/imaginary and go from there - if so I disagree.  excel has complex functions which work directly on complex numbers as posted from help below.

IMABS    Returns the absolute value (modulus) of a complex number
IMAGINARY    Returns the imaginary coefficient of a complex number
IMARGUMENT    Returns the argument theta, an angle expressed in radians
IMCONJUGATE    Returns the complex conjugate of a complex number
IMCOS    Returns the cosine of a complex number
IMDIV    Returns the quotient of two complex numbers
IMEXP    Returns the exponential of a complex number
IMLN    Returns the natural logarithm of a complex number
IMLOG10    Returns the base-10 logarithm of a complex number
IMLOG2    Returns the base-2 logarithm of a complex number
IMPOWER    Returns a complex number raised to an integer power
IMPRODUCT    Returns the product of two complex numbers
IMREAL    Returns the real coefficient of a complex number
IMSIN    Returns the sine of a complex number
IMSQRT    Returns the square root of a complex number
IMSUB    Returns the difference of two complex numbers
IMSUM    Returns the sum of complex numbers

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### RE: Taking the natural log of a negative number is Excel.

Just to put my previous comment in context, it is not so much the responses that I disagree with, but the original poster's 1/11 post implied the result of imln was just a text field which could not be used in calculations.  I thought in response it was important to emphasize that it is not a text field but a complex datatype complete with it's own functions which can be used in calcualtions.  Sorry I didn't mean to criticize anyone.

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### RE: Taking the natural log of a negative number is Excel.

The functions IMREAL and IMAGINARY also in the analysis toolpack will return teh real and imaginary coefficients of a complex number.  For example

IMREAL(IMLN(-15))=2.70805020110221
IMAGINARY(IMLN(-15))=3.14159265358979

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