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Question

In Argand plane, assume +x, -x, +y, -y as East, West, North & South respectively. A man walks a distance of 6 units from the Origin towards the north-east direction. From there, he walks a distance of 8 units towards the north-west direction to reach a point P. The position of P in the Argand plane is given by (a+ib)eiπ4. Then, a+b=


Solution


Let OA=6point A is given by 6eiπ4
z16eiπ4=|z1||6eiπ4|eiθ         (wheretanθ=86)
z16eiπ4=106(cosθ+isinθ)
z16eiπ4=106(610+i810)
z1=(6+8i)eiπ4
a+b=14

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