If z is a non - real complex number, then the minimum value of Im(z5)(Im(z))5 is
A
-1
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B
-2
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C
-4
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D
-5
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Solution
The correct option is C -4 Let z = a + ib, b ≠ 0 where Im (z) = b z5=(a+ib)5=a55C1a4bi+5C2a3b2i2+5C3a2b3i3+5C4i5b5 Im z5=5a4b−10a2b3+b5 y=Imz5Im5z=5(ab)4−10(ab)2+1 Let (ab)2=x(say),x∈R+ y=5x2−10x+1=5[x2−2x]+1 =5[(x−1)2]−4 Hence ymin=−4