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Consider the shape formed by the set of points z=ω-1/ω, where |ω|=2. Which of the following is incorrect?

Consider the shape formed by the set of points z=ω-1/ω, where |ω|=2. Which of the following is incorrect? Correct Answer major axis is of length=5/2

| ω|=2 ⇒ ω=2(cosθ+isinθ) ⇒ z=x+iy=2(cosθ+isinθ)-1/2(cosθ-isinθ)(⇒ |z|≤3) =3/2cosθ+i5/2sinθ⇒x2/(3/2)2+y2/(5/2)2=1 ⇒ ellipse ⇒ e2=1-(9/4)/(25/4)=16/25 ⇒ e=4/5.

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