Question

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

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

Answer 1

The correct option is D $(3+4i)e^{\frac{i\pi }{4}}$

Let OA=3, so that the complex number associated with A is $3e^{\frac{i\pi }{4}}$. If z is the complex number associated with P, then

$\frac{z-3e^{\frac{i\pi }{4}}}{0-3e^{\frac{i\pi }{4}}}=\frac{4}{3}{e}^{\frac{-i\pi }{2}}=-\frac{4i}{3}\Rightarrow 3z-9e^{\frac{i\pi }{4}}=12i{e}^{\frac{i\pi }{4}}\Rightarrow z=(3+4i)e^{\frac{i\pi }{4}}$