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Question

Question: \(8i\) =...

8i8i =

A

(1+i1−i)2+(1−i1+i)2\left( \frac{1 + i}{1 - i} \right)^{2} + \left( \frac{1 - i}{1 + i} \right)^{2}

B

1/5

C

1/10

D

–1/10

Answer

(1+i1−i)2+(1−i1+i)2\left( \frac{1 + i}{1 - i} \right)^{2} + \left( \frac{1 - i}{1 + i} \right)^{2}

Explanation

Solution

x+1x=2cos⁡θx + \frac{1}{x} = 2\cos\theta

⇒x2−2xcos⁡θ+1=0x=2cos⁡θ±4cos⁡2θ−42\Rightarrow x^{2} - 2x\cos\theta + 1 = 0x = \frac{2\cos\theta \pm \sqrt{4\cos^{2}\theta - 4}}{2}.