Circles centred at the origin in the z plane are mapped, Mechanical Engineering

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Circles centred at the origin in the z plane are mapped

Consider the mapping w = zn, where n is an integer (a generalization of the mapping w = z2). Use the polar representation of complex numbers to show that

(a) Circles centred at the origin in the z plane are mapped onto circles centred at the origin in the w plane.

(b) Straight lines passing through the origin intersecting with angle θ0 in the z plane are mapped onto straight lines passing through the origin in the w plane but intersecting at an angle nθ0.

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Mechanical Engineering: Circles centred at the origin in the z plane are mapped

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