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Prove that arg (z) + arg (vector z) = 2π.

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Prove that arg (z) + arg (vector z) = 2π.

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Let z = cosθ + i sinθ . 

Arg (z) = θ . 

vector z = cosθ - i sinθ = cos(2π- θ) +i sin(2π-θ). 

Arg ( vector z )= (2π-  θ).

Hence arg (z) + arg (vector z ) = 2π.

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