Complex exponential equation

rkj66 · **Joined:** Fri, 18 Dec 2009 14:15:51 UTC **Posts:** 6

Heya

I cant get my head around this one:

e^z = 1 , where z is a complex number

.. what is z ?

thanks

Denis · **Posted:** Tue, 14 Sep 2010 18:36:53 UTC

HINT: (anything)^0 = 1

Matt · **Joined:** Wed, 1 Oct 2003 04:45:43 UTC **Posts:** 9632

rkj66 wrote:

e^z = 1 , where z is a complex number

.. what is z ?

$e^z=e^{a+ib}=e^a(\cos b+i\sin b)=1$

In order for this to work, we must have a = 0 and $b=2\pi n$

rkj66 · **Joined:** Fri, 18 Dec 2009 14:15:51 UTC **Posts:** 6

Matt wrote:

rkj66 wrote:

e^z = 1 , where z is a complex number

.. what is z ?

$e^z=e^{a+ib}=e^a(\cos b+i\sin b)=1$

In order for this to work, we must have a = 0 and $b=2\pi n$

Thanks for the tip .. that helped. Now i wonder if there is a general solution for the equation:

e^z = c

??

Shadow · **Posted:** Thu, 16 Sep 2010 01:13:02 UTC

Denis wrote:

HINT: (anything)^0 = 1

Remember that complex numbers work differently, so 0 isn't the only thing...

Matt · **Joined:** Wed, 1 Oct 2003 04:45:43 UTC **Posts:** 9632

rkj66 wrote:

Now i wonder if there is a general solution for the equation:

e^z = c

Read about the complex logarithm. If you're taking a complex analysis course, then you'll learn about it eventually.

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