Question

A man walks a distance of 3 units from the origin towards the north-east $\left(N{45}^{\circ }E\right)$ direction. From there, he walks a distance of 4 units towards the north-west $\left(N{45}^{\circ }W\right)$ direction to reach a point P. Then the position of P in the Argand 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 $(3+4i)e^{i\pi /4}$

After first walk, the position is $(\frac{3}{\sqrt{2}},\frac{3}{\sqrt{2}})$
Hence he walks on $y=x$
After, this he walks 4 units perpendicular to $y=x$
Thus final position is
$(\frac{3-4}{\sqrt{2}},\frac{3+4}{\sqrt{2}})$
$=(3+4i)(1+i)\frac{1}{\sqrt{2}}$
$=(3+4i)e^{i\frac{\pi }{4}}$
Hence, option 'D' is correct.