JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Complex Numbers

A man walks a distance of 3 units from the origin towards the north-east

(N 4 5^{\circ} E)

direction. From there, he walks a distance of 4 units towards the north-west

(N 4 5^{\circ} W)

direction to reach a point

P

. Then the position of

P

in the Argand plane is

Answer: (D)

Solution

The first displacement is

3 e^{iπ /4}

(northeast at 45°).

The second displacement is 4 units northwest, which is at angle

\frac{3 π}{4}

from the positive x-axis, so

4 e^{i 3 π /4} = 4 i e^{iπ /4}

.

The position of P is:

z = 3 e^{iπ /4} + 4 i e^{iπ /4} = (3 + 4 i) e^{iπ /4}

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option