समीकरण `|z|-z = 1+2i` का हल है

Options

A. `(3)/(2) - 2i`
B. `(3)/(2) + 2i`
C. `2-(3i)/(2)`
D. इनमे से कोई नहीं

Answer

A

Explanation

`|z| - z = |x + iy| - (x + iy)`
` = 1+2i`
`rArr (sqrt(x^(2) + y^(2))-x)-iy = 1+2i`
`rArr sqrt((x^(2) + y^(2))) -x = 1`
तथा `-y = 2`
`rArr y = -2` तथा `sqrt((x^(2) + 4)) -x = 1`
या `x^(2) + 4 = (x +1)^(2) rArr x = (3)/(2)`
अतः `z = x + iy = (3)/(2) - 2i`