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# I need help with this problem

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Suppose that $$z$$ is a complex number such that  $$z^4 = \frac{64}{5}-\frac{48}{5}i$$. Find $$|z|$$.

Any help would be greatly appreciated!

Feb 2, 2020

#2
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I put the answer into Wolfram|Alpha and it says the answer is 2.

https://www.wolframalpha.com/input/?i=z%5E4%3D64%2F5-48%2F5i+find+%7Cz%7C

I have forgotten how to do it myself though.

Feb 2, 2020
#3
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The magnitude of the cn on the RHS is $$\displaystyle \sqrt{\left(\frac{64}{5}\right)^{2}+\left(\frac{48}{5}\right)^{2}}=16,$$

so the magnitude of z is the fourth root of 16, which is 2.

Feb 3, 2020
#4
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Wait, so are you saying that the magnitude of $$z$$ is the fourth root of the magnitude of $$z^4$$? Neat, will have to investigate to see why that is true. Thanks Guest!

Impasta  Feb 4, 2020