JEE Advanced 2008 Paper 2Question 1
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 in the direction of the vector $\hat{i}+\hat{j}$ and then it moves through an angle $\frac{\pi}{2}$ in anticlockwise direction on a circle with centre at origin, to reach a point $z_2$. The point $z_2$ is given by
Complex Numbers
Solution
$1+2i\to6+2i\to6+5i$; then $+\sqrt2\cdot\frac{1+i}{\sqrt2}$ gives $7+6i$; rotating by $\frac\pi2$ about the origin multiplies by $i$: $i(7+6i)=-6+7i$.