# Matrix Determinant / Complex numbers.

• Nov 21st 2008, 01:21 PM
battery2004
Matrix Determinant / Complex numbers.
Hello,

Ehh, i left this homework till the last day thinking its 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.jpghttp://img374.imageshack.us/images/thpix.gif

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

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

• Nov 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.
• Nov 21st 2008, 01:32 PM
Mathstud28
Quote:

Originally Posted by battery2004
Hello,

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

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

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

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}}\\