Matrix Determinant / Complex numbers.

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November 21st 2008, 01:21 PM
battery2004

Matrix Determinant / Complex numbers.

Hello,

Ehh, i left this homework till the last day thinking it`s not too hard, but actualy i have no clue how to completely solve any of them -

Determinant:
http://img374.imageshack.us/img374/9...ricaqh7.th.jpg http://img374.imageshack.us/images/thpix.gif

http://img355.imageshack.us/img355/539/kskva4.th.jpg http://img355.imageshack.us/images/thpix.gif

If anyone could solve just one of them it would be much appreciated!

Thanks, in advance.
November 21st 2008, 01:31 PM
Krizalid

For the first one, try to turn that matrix into a left triangular one, then you'll get easily the determinant.

As for the second question, it's just Euler's formula application.
November 21st 2008, 01:32 PM
Mathstud28

Quote:

Originally Posted by battery2004

Hello,

Ehh, i left this homework till the last day thinking it`s not too hard, but actualy i have no clue how to completely solve any of them -

http://img355.imageshack.us/img355/539/kskva4.th.jpg http://img355.imageshack.us/images/thpix.gif

If anyone could solve just one of them it would be much appreciated!

Thanks, in advance.

We know by Euler's Formula that $e^{ix}=\cos(x)+i\sin(x)$ . So $\begin{aligned}\sqrt[4]{7\left(\cos\left(\frac{\pi}{2}\right)+i\sin\left( \frac{\pi}{2}\right)\right)}&=\sqrt[4]{7}e^{\frac{\pi{i}}{8}}\\<br /> &=\sqrt[4]{7}\left(\cos\left(\frac{\pi}{8}\right)+i\sin\left (\frac{\pi}{8}\right)\right)<br /> \end{aligned}$

Do similarly for the second.