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
- Ab=-c
- Ba=0, b=c
- Ca=1, b=c
- 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