FP2 Loci

Two complex numbers, z and w, satisfy the inequalities:

|z-3-2i| =< 2 and |w-7-5i| =< 1
(=< represents less than or equal to inequality)

By drawing an Argand diagram, find the least possible value of |z-w|.

I sketched the diagram but can't make any further progress.

Original post by thers

Two complex numbers, z and w, satisfy the inequalities:

|z-3-2i| =< 2 and |w-7-5i| =< 1
(=< represents less than or equal to inequality)

By drawing an Argand diagram, find the least possible value of |z-w|.

I sketched the diagram but can't make any further progress.

Your sketch should be two discs.

Shortest distance would be a line perpendicular to the edge of each disc.

Can you see what to do now?

OP

Original post by ghostwalker

Your sketch should be two discs.

Shortest distance would be a line perpendicular to the edge of each disc.

Can you see what to do now?

Right I've worked it out now and got 2. It was just the |z-w| was confusing me.

Original post by thers

Right I've worked it out now and got 2.

Agreed.

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