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Question

Let z=x+iy and w=u+iv be two complex numbers which are connected by the transformation w = z+2z3. Then the curve in the z plane whose equation is |z3| = 1 is transformed into the w plane by

A
a circle
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B
a straight line
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C
an ellipse
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D
a parabola
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Solution

The correct option is D an ellipse
|z3|=1
(x3)2+y2=1
x=3+cosθ
y=sinθ
w=3+cosθ+isinθ+2cosθ+isinθ
w=3+3cosθisinθ
(u33)2+v2=1

Which represents an ellipse.

Hence, option C.

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