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Question

A man walks a distance of 3 units from the origin towards the north-east (N 45oE) direction. From there, he walks a distance of 4 units towards the north-west (N 45oW) direction to reach a point P. Then the position of P in the Argand plane is

A
3eiπ4+4i
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B
(34i)eiπ4
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C
(4+3i)eiπ4
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D
(3+4i)eiπ4
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Solution

The correct option is D (3+4i)eiπ4
Let OA=3, so that the complex number associated with A is 3eiπ4. If z is the complex number associated with P, then

z3eiπ403eiπ4=43eiπ2=4i33z9eiπ4=12ieiπ4z=(3+4i)eiπ4

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