# Help solving complex equation

• Mar 12th 2013, 03:20 PM
amro05
Help solving complex equation
hi there all

i need to find the value of x , y
where

Attachment 27503
• Mar 12th 2013, 03:52 PM
Plato
Re: Help solving complex equation
Quote:

Originally Posted by amro05
i need to find the value of x , y where
Attachment 27503

Complex exponentiation is difficult.

If each of $\displaystyle z~\&~w$ is a complex number then the principal value of $\displaystyle z^w$ is $\displaystyle \exp \left( {w\text{Log} (z)} \right)$

Now $\displaystyle \text{Log}(3+4i)=\ln (5) + \arctan \left( {\frac{4}{3}} \right)i$

Now what can you do with that?
• Mar 13th 2013, 10:15 AM
amro05
Re: Help solving complex equation
Quote:

Originally Posted by Plato
Complex exponentiation is difficult.

If each of $\displaystyle z~\&~w$ is a complex number then the principal value of $\displaystyle z^w$ is $\displaystyle \exp \left( {w\text{Log} (z)} \right)$

Now $\displaystyle \text{Log}(3+4i)=\ln (5) + \arctan \left( {\frac{4}{3}} \right)i$

Now what can you do with that?

thank you very mach for your help

I solved it by this way ( what do you think about it )

Attachment 27516