The closest distance of the origin from a curve given as `Abarz+barAz+AbarA=0` is: (A is a complex number).

Options

A. 1 unit
B. `("Re"(A))/(|A|)`
C. `(I_(m)(A))/(|A|)`
D. `1/2|A|`

Answer

D

Explanation

Let 'd' be the required distance. Then,
d=Length of the perpendicular from the origin on the line `Abarz+barAz+AbarA=0`
`rArr d=(A xx 0+barA xx 0 + AbarA)/(2|A|) = (|A|^(2))/(2|A|) = |A|/2`