SOLUTION: Find the fifth roots of 32(cos 280� + i sin 280�).

Question 984794: Find the fifth roots of 32(cos 280� + i sin 280�).
Answer by srinivas.g(540) (Show Source): You can put this solution on YOUR website!
i) Let z = 32(cos 280� + i sin 280�) = 32{cos(k*360� + 280�) + isin(k*360� + 280�)},
where k is an integer.
ii) ==> z^(1/5) = [32{cos(k*360� + 280�) + isin(k*360� + 280�)}]^(1/5)
==> z^(1/5) = 2[cos{(k*360� + 280�)/5} + isin{(k*360� + 280�)/5}]
[Application of De-Moievere's theorem]
==> z^(1/5) = 2[cos(72k + 56) + isin(72k + 56)]
We can now get the 5 roots, by assigning k = 0, 1, 2, 3 & 4
When k = 0, 1st root = 2(cos 56� + isin 56�)
When k = 1, 2nd root = 2(cos 128� + isin 128�)
When k = 2, 3rd root = 2(cos 200� + isin200�)
When k = 3, 4th root = 2(cos 272� + isin 272�)
When k = 4, 5th root = 2(cos 344� + isin344�)
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