The roots of the equation `(1+isqrt(3))^(x)-2^(x)=0` form

Options

A. an A.P.
B. a G.P.
C. an H.P.
D. none of these

Answer

A

Explanation

We have,
`(1+isqrt(3))^(x)-2^(x)=0`
`rArr (1/2+(isqrt(3))/(2))^(x)=1 rArr e^(ipix//3) = e^(i2rpi), r=0,+-1,+-2,……………`
`rArr x=6r`, where `r in Z`.
`rArr x =…….-12, -6,0,6,12`
Clearly, these are in A.P.