Solve this


If $\mathrm{a}$ and $\mathrm{b}$ are real numbers such that

$(2+\alpha)^{4}=a+b \alpha$, where $\alpha=\frac{-1+i \sqrt{3}}{2}$, then

$a+b$ is equal to :


  1. 57

  2. 33

  3. 24

  4. 9

Correct Option: 4,




$\Rightarrow \quad(2+\omega)^{4}=a+b \omega$

$\Rightarrow \quad 2^{4}+4 \cdot 2^{3} \omega+6 \cdot 2^{2} \omega^{3}+4 \cdot 2 \cdot \omega^{3}+\omega^{4}$ 

$=a+b \omega$

$\Rightarrow \quad 16+32 \omega+24 \omega^{2}+8+\omega=a+b \omega$

$\Rightarrow \quad 24+24 \omega^{2}+33 \omega=a+b \omega$

$\Rightarrow \quad-24 \omega+33 \omega=a+b \omega$

$\Rightarrow \quad a=0, b=9$


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now