Question

A particle $P$ starts from the point $z_0=1+2i,$ where $i=\sqrt{-1}.$ It moves first horizontally away from origin by $5$ units and then vertically away from origin by $3$ units to reach a point $z_1$. From $z_1$ the particle moves $\sqrt{2}$ units away from origin in the direction of $x=y$ and then it moves through an angle $\frac{\pi }{2}$ in anticlockwise direction on a circle with centre at origin to reach a point $z_2$. Then point $z_2$ is given by

• A. $6+7i$
• B. $-7+6i$
• C. $7+6i$
• D. $-6+7i$

Answer 1

The correct option is D $-6+7i$


$z_0\equiv (1+2i)$
$z_1\equiv (6+5i)$
after moving $\sqrt{2}$ unit in the direction of $x=y$
New position will be $(7+6i).$
Now, rotating about origin in anticlockwise direction, we get
$(7+6i)e^{i\pi /2}=-6+7i$