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COMEDK2017MathematicsComplex Number

If a, b, c are real numbers and is a complex cube root of unity such that a+b +c ²=0 , then

Options

  1. Ab=-c
  2. Ba=0, b=c
  3. Ca=1, b=c
  4. Da=b=c

Correct answer

D. a=b=c

Step-by-step solution

We have, a+b +c ²=0 aligned & a+b (- 1 2 + i 3 2 )+c (- 1 2 - i 3 2 )=0 & (a- b 2 - c 2 )+i ( 3 b 2 - 3 c 2 )=0+0 i & Real part a= b+c 2 & Imaginary parts b=c & a=b=c aligned

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