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Q.

A man walks a distance of 3 units from the origin towards the north-east (N   450    E)  direction. From there, he walks a distance of 4 units towards the north-west (N   450    W)  direction to reach a point P . Then the position of P  in the Argand plane is:

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a

3eiπ/4+4i

b

(3−4i)eiπ/4

c

(4+3i)eiπ/4

d

(3+4i)eiπ/4

answer is D.

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Detailed Solution

Let OA=3 , so that the complex number associated with A  is 3eiπ/4 . If z is the complex number associated with P , then     z−3eiπ/40−3eiπ/4=43e−π/2=−4i3 ⇒           3z−9eiπ/4=12ieiπ/4 ⇒                 z=(3+4i)eiπ/4
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