On the argand plane, let α=-2+3 z, β=-2-3 z &|z|=1. Then the correct statement is -

Question

On the argand plane, let α=-2+3 z, β=-2-3 z &|z|=1. Then the correct statement is - (A) α moves on the circle, centre at (-2,0) and radius 3 (B) α β describe the same locus (C) α β move on different circles (D) α-β moves on a circle concentric with |z|=1

Tardigrade Admin · Accepted Answer

α=-2+3 z α+2=3 z |α+2|=3|z| (x+2)2+y2=9 Similarly β=-2-3 z ⇒ β+2=-3 z ⇒ |β+2|=|-3 z| (x+2)2+y2=9 Now α-β=6 z ⇒|α-β|=6|z| so (α-β) moves on a circle with centre as origin and radius 6 .

Q. On the argand plane, let $α = - 2 + 3 z, β = - 2 - 3 z &∣ z ∣ = 1$ . Then the correct statement is -

$α$ moves on the circle, centre at $(- 2, 0)$ and radius 3

$α & β$ describe the same locus

$α & β$ move on different circles

$α - β$ moves on a circle concentric with $∣ z ∣ = 1$

Q. On the argand plane, let α=−2+3z,β=−2−3z&∣z∣=1. Then the correct statement is -

α moves on the circle, centre at (−2,0) and radius 3

α&β describe the same locus

α&β move on different circles

α−β moves on a circle concentric with ∣z∣=1

α=−2+3z α+2=3z ∣α+2∣=3∣z∣ (x+2)2+y2=9 Similarly β=−2−3z ⇒β+2=−3z ⇒∣β+2∣=∣−3z∣ (x+2)2+y2=9 Now α−β=6z⇒∣α−β∣=6∣z∣ so (α−β) moves on a circle with centre as origin and radius 6 .

Q. On the argand plane, let $α = - 2 + 3 z, β = - 2 - 3 z &∣ z ∣ = 1$ . Then the correct statement is -

$α$ moves on the circle, centre at $(- 2, 0)$ and radius 3

$α & β$ describe the same locus

$α & β$ move on different circles

$α - β$ moves on a circle concentric with $∣ z ∣ = 1$