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Question

If z=4cosθ(cosθ+isinθ), θR, then the locus of z on the argand plane is
  1. an ellipse with centre (0,2)
  2. a circle with centre (0,2)
  3. an ellipse with centre (2,0)
  4. a circle with centre (2,0)


Solution

The correct option is D a circle with centre (2,0)
z=4cosθ(cosθ+isinθ)z=4cos2θ+i(4sinθcosθ)Let z=x+iyx=4cos2θ=2(1+cos2θ)
and y=22sinθcosθ=2sin2θ
(x2)2+y2=4

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