How do I find the answer to e^i(pi/18) *without* using a calculator.

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- May 26th 2006, 08:08 PMchanceyComplex problem
How do I find the answer to e^i(pi/18) *without* using a calculator.

Thanks - May 27th 2006, 05:47 PMThePerfectHackerQuote:

Originally Posted by**chancey**

$\displaystyle e^{i(\pi/18)}=\cos (\pi/18)+i\sin(\pi/18)$

All you need to do is find what (co)sine of $\displaystyle \pi/18$ is, you can do this by using the third angle identity,

$\displaystyle

\cos 3\theta=4\cos^3 \theta-3\cos \theta

$

Which reduces to solving a cubic equation. - May 27th 2006, 06:13 PMchanceyQuote:

Originally Posted by**ThePerfectHacker**

- May 27th 2006, 06:28 PMThePerfectHackerQuote:

Originally Posted by**chancey**

You have,

$\displaystyle \frac{ \sqrt{3} }{2}=4x^3-3x$

Maybe time later I will solve this cubic, I predict it will look messy. - May 27th 2006, 07:27 PMchancey
Ahh, I see. So there is no formula(s) for solving any complex exponential? What if I had something really messy like, $\displaystyle e^{0.155i}$?

And yes, when that cubic equation is solved it gives the correct answer