Find the least possible value of ##|z-w|## -Complex numbers

[chwala]

Homework Statement

Two complex numbers $z$ and $w$ satisfy the inequalities $|z-3-2i|≤2$ and $|w-7-5i|≤1$. By drawing an argand diagram, find the least possible value of $|z-w|$

There is a similar post to this posted in 2010 on physicsforums and the OP did not seem to have posted his working to solution.(I wanted to make some comments on that but the post is not open to further replies)

Relevant Equations

Complex numbers.

OK, here once a sketch is done, we have two circles $c_1$ and $c_2$ with centre's $c_1 (3,2)$ and $c_2 (7,5)$ having radius $2$ and $1$ respectively. It follows that the distance between the the two centre's is given by $L=\sqrt {(7-3)^2+(5-2)^2}$=$5$
Now, the least possible value $|z-w|=5-(2+1)=2$

Supposing, just to explore this further, they want us to find the greatest distance, then we may say that the greatest ditance of $|z-w|=5+1+2=8$

I would appreciate your thoughts on this...cheers guys

 

[BvU]

No thoughts, except: 'where's the picture?'
Well, perhaps one small second thought: what 2010 thread ?

$\$

 

[chwala]

No thoughts, except: 'where's the picture?'
Well, perhaps one small second thought: what 2010 thread ?

$\$

Bvu...you can tell from my working that i know how the pic looks like...This is the 2010 post;

 

[SammyS]

Homework Statement:: Two complex numbers $z$ and $w$ satisfy the inequalities $|z-3-2i|≤2$ and $|w-7-5i|≤1$. By drawing an argand diagram, find the least possible value of $|z-w|$

There is a similar post to this posted in 2010 on physicsforums and the OP did not seem to have posted his working to solution.(I wanted to make some comments on that but the post is not open to further replies)

This appears to be the link for that closed PF thread:

https://www.physicsforums.com/threads/complex-numbers-finding-the-least-value-of-z-w.446274/

 

[Office_Shredder]

I think it's pretty standard to not care if a thread was made twelve years ago, and just make a new one instead.

 

[BvU]

This is the 2010 post;

Haha, as if I care for a screen shot. My angle was: if you refer to something, don't let others search for it but provide a link. @SammyS understood.

you can tell from my working that i know how the pic looks like

Same difference: yes I can, but maybe others can not.

I think it's pretty standard to not care if a thread was made twelve years ago, and just make a new one instead.

Especially the bad and messy ones

$\$

 

[haruspex]

Supposing, just to explore this further, they want us to find the greatest distance, then we may say that the greatest distance of $|z-w|=5+1+2=8$

Yes, of course.

 

[chwala]

Thanks haruspex...cheers mate...