Find the Area bounded by complex numbers `arg|z|lepi/4` and `|z-1|lt|z-3|`

Explanation

`|arg z| lt pi//4`
`-pi//4 lt arg z lt pi//4`
Which represents the region shown in the figure.

`|z-1| lt |z - 3|`
`rArr (x-1)^(2) + y^(2) lt (x -3)^(2) + y^(2)`
`rArr x lt 2`
Common region of (1) and (2) is shown in the figure .

Area of the shaded region is `(1)/(2)(4)(2) = 4` sq. units