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MCQ
Fill in the Blanks
If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.
Options
Re (z) = 0
Im (z) = 0
Re (z) > 0, Im (z) > 0
Re (z) > 0, Im (z) < 0
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Solution
If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then Im (z) = 0.
Explanation:
On simplification, we get
z = `2 ""^5"C"_0 sqrt(3)^2/2 + ""^5"C"_2 sqrt(3)^3/2 i^2/2 + ""^5"C"_4 sqrt(3)/2 i^4/2`
Since i2 = –1 and i4 = 1
z will not contain any i and hence Im (z) = 0.
Concept: Binomial Theorem for Positive Integral Indices
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