A man walks a distance of 3 units from the origin towards north-east to reach position A. from there he walks a distance of 4 units towards North west to reach position P. Then position of P in argand plane is

Options

A. `3e^(I pi 4)+4i`
B. `(3-4 i)e^(I pi 4)`
C. `(4 + 3 i)e^(I pi 4)`
D. `(3+4i )e^(I pi 4)`

Answer

D

Explanation

Let OA=3 so that the complex number associated with A si `3e^( ipi//4)`, If z is the complex number associated with P, then
`(z-3e^(ipi//34))/(0-3e^(ipi//4))=4/3e^(-pi//2)=-(4 i)/(3)`
`rArr 3 z-9e^(ipi//4)=12 ie^(ipi//4)`
`rArr z= (3+ 4 i)e^(ipi//4)`