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Math Help - Matrix Determinant / Complex numbers.

  1. #1
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    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:




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

    Thanks, in advance.
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  2. #2
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    Krizalid's Avatar
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    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.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by battery2004 View Post
    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 -





    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.
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