Which of the following represents a points in an Argand pane, equidistant from the roots of the equation `(z+1)^4=16 z^4?` `(0,0)` b. `(-1/3,0)` c. `(1/3,0)` d. `(0,2/(sqrt(5)))`

Options

A. `(0,0)`
B. `(-(1)/(3),0)`
C. `((1)/(3),0)`
D. `(0,(2)/(sqrt(5)))`

Answer

C

Explanation

`((z+1)/(z))^(4) = 16`
`rArr (z+1)/(z)= pm2,pm2i`
The roots are 1, `-1//3,(-1//5-(2//5)i),` and `(-1//5 + (2//5)i)`.
Note that `(-1//3,0)` are (1,0) are equidstant form `(1//3,0)` and since it lies on the perpendicular bisector of Ab , It will be equidistant form A and B also.