# Thread: Matrix Determinant / Complex numbers.

1. ## 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:

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

2. 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.

3. 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 -

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

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