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Question

If |z|=2 and arg(z)=π4, find z.

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Solution

Let z=r (cos θ+i sin θ)|z|=r=2 and θ=π4z=2[cosπ4+i sinπ4] [ z=r (cosθ+i sinθ)]=2[12+i 12]=2(1+i)


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