Question

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 Arg and plane is

• A. $3e^{i \pi/4}+4i$
• B. $(3-4i)e^{i \pi/4}$
• C. $(4+3i)e^{i \pi/4}$
• D. $(3+4i)e^{i \pi/4}$

Answer 1

The Correct Option is D

Let OA = 3, so th a t the complex number associated with
A is 3e$^{i \pi/4 }$. If z is the complex number associated with P,
then
$\frac{z-3e^{i \pi/4}}{0-3e^{i \pi/4}}=\frac{4}{3} e^{-i \pi/2}=-\frac{4i}{3}$
'
$\Rightarrow \, 3z-9e^{i \pi/4}=12ie^{i \pi/4}$
$\Rightarrow \, \, \, \, z=(3+4i)e^{i \pi/4}$