Question

In G.P. the first term and common ratio are both $\frac{1}{2}(\sqrt{3}+i)$, then the absolute value of its $n^{th}$ term is

• A. 1
• B. $2^n$
• C. $4^n$
• D. none

Answer 1

The correct option is A 1

GIven

First term $a=\frac{1}{2}(\sqrt{3}+i)$

Common ratio $r=\frac{1}{2}(\sqrt{3}+i)$

$n^{th}$ term $T_n=a{r}^{n-1}=(\frac{\sqrt{3}+i}{2}{)}^n=e^{i\frac{n\pi }{6}}$

So, absolute value of this term is 1