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Question Number 25000 by ErickDN last updated on 30/Nov/17

$$findx,yfromtheequation:$$$$\frac{1}{2}x-yi+\frac{1}{1+i}={(\sqrt{1+{\omega }^8}+\sqrt{1+{\omega }^{10}})}^4$$$$$$

Answered by ajfour last updated on 01/Dec/17

$$\Rightarrow \frac{x}{2}-iy+\frac{1-i}{2}={(\sqrt{-\omega }+\sqrt{-{\omega }^2})}^4$$$$\frac{x}{2}-iy=\frac{-1+i}{2}+{(e^{-\frac{i\pi }{6}}+e^{\frac{i\pi }{6}})}^4$$$$\frac{x}{2}-iy=\frac{-1+i}{2}+9$$$$\Rightarrow x=17;y=-\frac{1}{2}.$$

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