Let a,b ` in ` R and `a^(2) + b^(2) ne 0` . Suppose `S = { z in C: z = (1)/(a+ ibt),t in R, t ne 0}`, where `i= sqrt(-i)`. If `z = x + iy` and z in S, then (x,y) lies on

Options

A. the x-axis for `a ne 0, b=0`
B. the y-axis for `a ne 0, b=0`
C. the y-axis for `a ne 0, b ne 0`
D. the `x-`axis for a=0, `b ne 0`

Explanation

We have, `z=1/(a+ibt)`
`z=1/(a+ibt)`
`rArr x+iy=(a-ibt)/(a^(2)+b^(2)t^(2))`
`rArr x=a/(a^(2)+b^(2)t^(2))` and `y=-(bt)/(a^(2)+b^(2)t^(2))`
`rArr xbt=-ay`
`rArr y=0`, If `a ne 0` and `b ne 0`, the locus is y-axis.