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On the Argand plane ,let z(1) = - 2+ 3...

On the Argand plane ,let `z_(1) = - 2+ 3z,z_(2)= - 2-3z` and `|z| = 1`. Then

A

`z_(1)` moves on circle with centre at `(-2,0)` and radius 3

B

`z_(1)` and `z_(2)` describle the same locus

C

`z_(1)` and `z_(2)` move on differenet circles

D

`z_(1)-z_(2)` moves on a circle concetric with `|z|=1`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
We have `z_(1) + 2= 3z and -z_(2)-2=3z`
`rArr |z_(1) + 2| = 3|z| =3`
` and `z_(2) + 2 = - 3z`
`rArr |z_(2) +2|=|-3z|=3`
`Thus `z_(1) ` and `z_(2)` describe the same circle having centre at '-2' and radius'3'
Now, `z_(1) - z_(2) = 6z`
`rArr |z_(1)-z_(2)| = 6|z|=6`
So, `(z_(1) -z_(2))` moves on a circle with centre as origin and radius 6.
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