find-x-y-from-the-equation-1-2-x-yi-1-1-i-1-8-1-10-4-

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

f i n d x, y f r o m t h e e q u a t i o n :

\frac{1}{2} x - y i + \frac{1}{1 + i} = {(\sqrt{1 + ω^{8}} + \sqrt{1 + ω^{10}})}^{4}

Answered by ajfour last updated on 01/Dec/17

\Rightarrow \frac{x}{2} - i y + \frac{1 - i}{2} = {(\sqrt{- ω} + \sqrt{- ω^{2}})}^{4}

\frac{x}{2} - i y = \frac{- 1 + i}{2} + {(e^{- \frac{i π}{6}} + e^{\frac{i π}{6}})}^{4}

\frac{x}{2} - i y = \frac{- 1 + i}{2} + 9

\Rightarrow x = 17; y = - \frac{1}{2} .

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