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Sir please tell me question no 11 of attached image

Pushkar Kumar , 5 Years ago
Grade 12
anser 1 Answers
Samyak Jain

Last Activity: 5 Years ago

z = (1 + cos8\pi/5) + sin8\pi/5.
Use 1 + cos2\theta = 2 cos2\theta  and  sin2\theta = 2 sin\theta cos\theta.
z = 2 cos24\pi/5 + i.2 sin4\pi/5 cos4\pi/5 = 2 cos4\pi/5 (cos4\pi/5 + i.sin4\pi/5).
Already 4\pi/5 lies in the interval (– \pi, \pi).
So, principal value of arg(z) is 4\pi/5.

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