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Q.

Two points P and Q in the Argand diagram represent z and 2z + 3 + i. If P moves on a circle with centre at the origin and radius 4, then the locus of Q is a circle with centre

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a

(-3, 1)

b

(3, 1)

c

(0, 0)

d

(2, -3)

answer is A.

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Detailed Solution

 P=z ,Q=2z+3+i= z1

P lies on a circle with centre = (0, 0) , radius = 4

⇒ |z|=4

 Let z1=2z+3+i

⇒z1-(3+i)=2z ⇒z1-(3+i)=2|z| z1-(3+i)=8

Q(z1) lies on a circle with centre (3, 1)

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