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If z=i(1+3) then z4+2z3+4z2+5 is equal to-

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a

5

b

-5

c

23i

d

-23i

answer is A.

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Detailed Solution

z=i(1+3)=−1+3i=2ωwhere ω≠1 is a cube root of unity∴ z4+2z3+4z2+5=(2ω)4+2(2ω)3+4(2ω)2+5=16ω4+16ω3+16ω2+5=16ω+1+ω2+5=16(0)+5=5

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