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Question : 10 of 160
Marks:
+1,
-0
Solution:
Given
x and
y are two complex number with
|x|=|y|=1 and
x=ei2αy‌=ei.3β,‌ where ‌α+β=‌⇒‌‌x6‌=(ei2α)6=ei.12αy4‌=(ei.3β)4=ei.12βSo,
x6⋅y4=ei.12α⋅ei,12β=ei.12(α+β)Since,
α+β=‌⇒‌‌x6⋅y4=ei.12‌=ei‌and
‌=e−i⋅‌⇒x6⋅y4+‌‌=ei⋅‌+e−i⋅‌‌=2‌cos‌=1
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