If-z-2-then-the-points-representing-the-complex-numbers-1-5z-will-lie-on-a-1-Circle-2-Straight-line-3-Parabola-4-Ellipse-

Question Number 19629 by Tinkutara last updated on 13/Aug/17

If ∣ z ∣ = 2, then the points representing

the complex numbers - 1 + 5 z will lie

on a

(1) Circle

(2) Straight line

(3) Parabola

(4) Ellipse

Answered by ajfour last updated on 13/Aug/17

x + iy = - 1 + 5 \times {2 e}^{i θ}

x - iy = - 1 + 5 \times {2 e}^{- i θ}

(x + 1 + iy) (x + 1 - iy) = 100

{(x + 1)}^{2} + y^{2} = 10^{2}

They lie on a circle then . (1) .

Commented by Tinkutara last updated on 13/Aug/17

Thank you very much Sir!