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# what is as a complex number?

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what is $$\sqrt(2) ^ {(\frac{7\pi i}{4})}$$ as a complex number?

Apr 23, 2019

#1
+6196
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$$\text{do you mean}\\ \sqrt{2^{i7\pi/4}}$$

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Apr 23, 2019
#2
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nope

Guest Apr 24, 2019
#3
+110811
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$$y=(\sqrt2)^{(\frac{7\pi i}{4})}\\ y=2^{(\frac{7\pi }{8}i)}\\ log y=log 2^{(\frac{7\pi }{8}i)}\\ ln y=(\frac{7\pi }{8}i) ln 2\\ e^{ln y}=e^{(\frac{7ln 2\pi }{8}i) }\\ y=e^{(\frac{7(ln 2)\pi }{8})i }\\ y=cos(\frac{7(ln 2)\pi }{8})+isin(\frac{7(ln 2)\pi }{8})$$

You had better check that very carefully.

Apr 24, 2019