Question

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

(a) eccentricity=4/5

(b) |z|≤3

(c) shape is an ellipse

(d) major axis is of length=5/2

I have been asked this question during an interview.

The query is from Regions in the Complex Plane in chapter Complex Numbers of Engineering Mathematics

Answer 1

Correct option is (d) major axis is of length=5/2

To elaborate: | ω|=2 ⇒ ω=2(cosθ+isinθ) ⇒ z=x+iy=2(cosθ+isinθ)-1/2(cosθ-isinθ)(⇒ |z|≤3)

=3/2cosθ+i5/2sinθ⇒x^2/(3/2)^2+y^2/(5/2)^2=1 ⇒ ellipse ⇒ e^2=1-(9/4)/(25/4)=16/25

⇒ e=4/5.