Hi

Can someone please help me on the following question

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

thanks

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- Feb 21st 2009, 08:37 AMrpatelcomplex number exponential form
Hi

Can someone please help me on the following question

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

thanks - Feb 21st 2009, 08:52 AMPlato
$\displaystyle e^{x + yi} = \left[ {e^x \cos (y)} \right] + i\left[ {e^x \sin (y)} \right]$

- Feb 21st 2009, 09:27 AMrpatel
thats in polar form though. How would you get it into catesian ?

- Feb 21st 2009, 09:38 AMPlato
- Feb 21st 2009, 09:42 AMMoo
It's not because there are exponentials that it is still in polar form.

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

But $\displaystyle e^x$ is a real number, for any real x.

So $\displaystyle e^x \cos(y)$ is real and $\displaystyle e^x \sin(y)$ is real.

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