If z = 3 2 + i 2   i = - 1 ,   then 1 + i z + z 5 + i z 8 9 is equal to:

If z=32+i2 i=-1,  then 1+iz+z5+iz89 is equal to:
  1. -1
  2. 1
  3. 0 
  4. -1+2i9

Solution

z=32+i2  ∴iz=-12+32i=ω
∴1+iz+z5+iz89=1+ω+ω5i5+i×ω8i89 
=1+ω-iω2+iω29
=-ω29=-ω18
= -1

Asked in: JEE Main 2019 (08 Apr Shift 2)

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