# complex number exponential form

• Feb 21st 2009, 08:37 AM
rpatel
complex number exponential form
Hi

Write w=e^1+3i in Cartesian form.

thanks
• Feb 21st 2009, 08:52 AM
Plato
$e^{x + yi} = \left[ {e^x \cos (y)} \right] + i\left[ {e^x \sin (y)} \right]$
• Feb 21st 2009, 09:27 AM
rpatel
thats in polar form though. How would you get it into catesian ?
• Feb 21st 2009, 09:38 AM
Plato
Quote:

Originally Posted by rpatel
thats in polar form though. How would you get it into catesian ?

I really don't understand your confusion.
The following is produced by the CAS MathCad.
• Feb 21st 2009, 09:42 AM
Moo
Quote:

Originally Posted by rpatel
thats in polar form though. How would you get it into catesian ?

It's not because there are exponentials that it is still in polar form.

In cartesian form, it would be like $a+ib$, where a and b are real numbers.

But $e^x$ is a real number, for any real x.
So $e^x \cos(y)$ is real and $e^x \sin(y)$ is real.

The formula Plato gave is, without any doubt, a cartesian form, the one corresponding to $e^{x+iy}$.