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If 1 is a cube root of unity, then what are the solution of (z-100)^3+1000=0 ?

Options

  1. A10(1- ), 10 (10- ^2 ), 100
  2. B10(10- ), 10 (10- ^2 ), 90
  3. C10(1- ), 10 (10- ^2 ), 1000
  4. D(1+ ), (10+ ^2 ),-1

Correct answer

B. 10(10- ), 10 (10- ^2 ), 90

Step-by-step solution

aligned & (z-100)^3+1000=0 & (z-100)^3=-1000=(-10)^3 & z-100=-10 & z=90 & z-100=10 w z=100-10 w & z-100=-10 w^2 & z=100-10 w^2 . aligned

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