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Question

Mathematics Question on Complex Numbers and Quadratic Equations

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

3eiπ/4+4i3e^{i \pi/4}+4i

B

(34i)eiπ/4(3-4i)e^{i \pi/4}

C

(4+3i)eiπ/4(4+3i)e^{i \pi/4}

D

(3+4i)eiπ/4(3+4i)e^{i \pi/4}

Answer

(3+4i)eiπ/4(3+4i)e^{i \pi/4}

Explanation

Solution

Let OA = 3, so th a t the complex number associated with
A is 3eiπ/4^{i \pi/4 }. If z is the complex number associated with P,
then
z3eiπ/403eiπ/4=43eiπ/2=4i3\frac{z-3e^{i \pi/4}}{0-3e^{i \pi/4}}=\frac{4}{3} e^{-i \pi/2}=-\frac{4i}{3}
'
3z9eiπ/4=12ieiπ/4\Rightarrow \, 3z-9e^{i \pi/4}=12ie^{i \pi/4}
z=(3+4i)eiπ/4\Rightarrow \, \, \, \, z=(3+4i)e^{i \pi/4}