The shaded region, where $P \equiv ( - 1,\ 0),\ Q \equiv ( - 1 + \sqrt{2},\ \sqrt{2})$ $R \equiv \left( - 1 + \sqrt{2},\ - \sqrt{2} \right),\ S \equiv (1,\ 0)$ is represented by [image:5_image2.emf]

Question

Dr. Abubacker · Accepted Answer

(a)
Here, $|PQ| = |PS| = |PR| = 2$
$	herefore$ Shaded part represents the external part of circle having centre (-1, 0) and radius 2
[image:5_image8.jpeg]
As we know equation of circle having centre $z_{0}$ and radius $r$, is
$\left| z - z_{0} ight| = r$
$	herefore\ \ \ \ \ \ \ \ \ \ |z—( - 1 + 0i)| > 2$
$\Rightarrow \ \ \ \ |z + 1| > 2$ …(i)
Also, argument of $z + 1$ with represent to positive direction of $x$-axis is $\pi/4\$
$	herefore\ \ \arg{(z + 1) \leq \frac{\pi}{4}}$
And argument of $z + 1$ in anti-clockwise direction is $–\pi/4$.
$	herefore\ \ \ \ \ \ \ \ \ \ \  - \frac{\pi}{4} \leq \arg(z + 1)$
$\Rightarrow \ \ \ \ \ \ \ |\arg(z + 1)| \leq \frac{\pi}{4}$

Q. The shaded region, where $P \equiv ( - 1,\ 0),\ Q \equiv ( - 1 + \sqrt{2},\ \sqrt{2})$ $R \equiv \left( - 1 + \sqrt{2},\ - \sqrt{2} \right),\ S \equiv (1,\ 0)$ is represented by

Explanation

Reviewed by Dr. Abubacker

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