If `sqrt(3)+i=(a+i b)//(c+i d)` , then find the value of `tan^(-1)(b//a)tan^(-1)(d//c)dot`

Options

A. `pi/3`
B. `pi/6`
C. `-pi/6`
D. `(5pi)/6`

Answer

B

Explanation

We have,
`sqrt(3)+i=(a+ib)(c+id)`
`rArr sqrt(3)+i=(ac-bd)+i(ad+bc)`
`rArr sqrt(3)=ac-bd` and `1=ad+bc`
Now, `therefore tan^(-1)b/c +tan^(-1)d/c=tan^(-1)((b/a+d/c)/(1-b/a xx d/c))` `[therefore bd lt ac]`
`rArr tan^(-1)b/a + tan^(-1)d/c= tan^(-1)(ad+bc)(ac-bd) = tan^(-1) (1/sqrt(3))=pi/6`