# Thread: complex number exponential form

1. ## complex number exponential form

Hi

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

thanks

2. $e^{x + yi} = \left[ {e^x \cos (y)} \right] + i\left[ {e^x \sin (y)} \right]$

3. thats in polar form though. How would you get it into catesian ?

4. 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.

5. 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 $e^{x+iy}$.