JEE Advanced 2007 Paper 1Question 1
A man walks a distance of 3 units from the origin towards the north-east ($N\,45^\circ E$) direction. From there, he walks a distance of 4 units towards the north-west ($N\,45^\circ W$) direction to reach a point $P$. Then the position of $P$ in the Argand plane is
Complex Numbers
Solution
North-east step: $3e^{i\pi/4}$. North-west step: $4e^{i3\pi/4}=4ie^{i\pi/4}$. So $P=(3+4i)e^{i\pi/4}$.