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### Natural log of complex numbers

```
Date: 8/31/96 at 12:28:13
From: Anonymous
Subject: Natural log of complex numbers

e^i*Pi=isin(Pi) + cos (Pi) = -1

If I square both sides:

e^2i*Pi= 1

Taking the natural log,

2i*Pi=0 !

But how can the product of three constants = 0?

David
```

```
Date: 9/13/96 at 21:28:1
From: Doctor Ceeks
Subject: Re: Natural log of complex numbers

Hi,

The natural logarithm is not well-defined on the complex plane for
the same reason that the exponention function is not one to one.

Thus, a=b does not imply ln(a)=ln(b).

Your argument is similar to the following:

4 = 4.

Take square roots.

-2 = 2 !

-Doctor Ceeks,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Imaginary/Complex Numbers

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