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Use DeMoivre's Theorem to find.?
((1/2)+(√3/2))^5
1 Answer
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- Anonymous1 decade agoFavorite Answer
I am assuming that we need to find:
(1/2 + i√3/2)^5.
Note that:
(1/2 + i√3/2)^5
= [1/2 * (1 + i√3)]^5
= 1/32 * (1 + i√3)^5.
Then, in polar form:
1 + i√3 = 2(cos π/3 + i sin π/3).
Therefore:
(1/2 + i√3/2)^5
= 1/32 * (1 + i√3)^5
= 1/32 * [2(cos π/3 + i sin π/3)]^5
= 1/32 * 2^5 * [cos(5 * π/3) + i sin (5 * π/3)]
= cos 5π/3 + i sin 5π/3
= 1/2 - i√3/2. <== ANSWER
I hope this helps!
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