Question

Find the area bounded by $arg\left|z\right|\le \pi /4$ and $|z-1|<|z-3|$.

• A. $16$ sq unit.
• B. $8$ sq unit.
• C. $4$ sq unit.
• D. $2$ sq unit.

Answer 1

The correct option is C $4$ sq unit.

$\left|argz\right|<\pi /4$
$-\pi /4<argz<\pi /4$ (1)
which representing the region shown in Fig
$|z-1|<|z-3|$
$⟹(x-1{)}^2+y^2<(x-3{)}^2+y^2$
$⟹x<2$ (2)
Common region of (1) and (2) is given in Fig.
Area of the shaded region is $\frac{1}{2}\left(4\right)\left(2\right)=4$ sq unit.
Ans: C