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Question: Answered & Verified by Expert
If z=32+i2 i=-1,  then 1+iz+z5+iz89 is equal to:
MathematicsComplex NumberJEE MainJEE Main 2019 (08 Apr Shift 2)
Options:
  • A -1
  • B 1
  • C 0 
  • D -1+2i9
Solution:
1159 Upvotes Verified Answer
The correct answer is: -1
z=32+i2  ∴iz=-12+32i=ω
∴1+iz+z5+iz89=1+ω+ω5i5+i×ω8i89 
=1+ω-iω2+iω29
=-ω29=-ω18
= -1

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