Question

If ${(1+i\sqrt{3})}^9=a+ib,a,b\in R,$ then the value of $b$ is

• A. 29
• B. $-29$
• C. 0
• D. None of these

Answer 1

Answer: (C)

${(1+i\sqrt{3})}^9=2^9{\left[\frac{1}{2}+\frac{i\sqrt{3}}{2}\right]}^9$
$=2^9{\left[\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}\right]}^9$
$=2^9[\cos 3\pi +i\sin 3\pi ]$
[by De-moiver theorem]
$=2^9[-1+i0]$
$=-2^9=a+ib$
$\Rightarrow$ $b=0$