complex numbers related question

Question

if   x = [ (√ 3 / 2)  +  ( i/ 2) ] then  x²  is  :

 

1.    -1
2.     1 
3.    -i
4.     i

%MCEPAS  , thenTEBIN%

Answer 1

I think that you mean x³, not x²     

 

[√3/2 + i/2]² = 3/4 + (√3/2)i - 1/4

 

                         = 1/2 + (√3/2)i

 

So [√3/2 + i/2]³ = [1/2 + (√3/2)i][√3/2 + i/2]

 

                               = √3/4 + (3/4)i + (1/4)i + (√3/4)i²

 

                               = √3/4 + i - √3/4

 

                               = i

 

The answer is choice (4), assuming that we are evaluating x³.

 

 

Answer 2

We square both sides of equation.

 

x² = [(√(3) + i) / 2] * [ (√(3) + i) / 2]

 

x² = (3 + 2i√(3) + i²) / 4

 

x² = (3 + 2i√(3) - 1) / 4

 

x² = (2i√(3) + 2) / 4

 

 

This is what you will obtain, but I believe the answer choices are not right.