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chwala

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- 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

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

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