Question

The set of points on an Argand diagram which satisfy both $\left|z\right|\le 4\&Argz=\frac{\pi }{3}$ is

• A. a circle & a line
• B. a radius of a circle
• C. a sector of a circle
• D. an infinite part line

Answer 1

The correct option is B a radius of a circle

$\Rightarrow \left|z\right|\le 4\xi Argz=\frac{\pi }{3}$

For all points on the line

$\Rightarrow \left|\overline{z}\right|\le 4$ and $arg\left(\overline{z}\right)=\frac{\pi }{3}$

As this is a circle of radius 4. For all points inside the circle and on it,

$x^2+y^2\le 4$ or $\left|\overline{z}\right|\le 4$

And the vector its indined at an angle $\frac{\pi }{3}$

w.r.t $x-axis.$

Hence, the answer is a radius of a circle.