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For all complex numbers z 1 , z 2 satisfying l z 1 l= 12 lz 2 – 3 l=5 the minimum value of l z 1 - z 2 l is ??? plz explain also

For all complex numbers z1, z2 satisfying
l z1 l= 12     lz2 – 3 l=5
the minimum value of l z1 - z2 l is ???
plz explain also

Grade:12th pass

2 Answers

Aditya Gupta
2081 Points
4 years ago
We know that |z-0|=12 and |z-3|= 5 represent circles with centre and radius 0, 12 and 3, 5 respectively.
So, if you draw the circles in argand plane, you will see that the minimum distance occurs when z1 and z2 are along the x axis, so that z1= 8 and z2= 12
Since |z1-z2| represents the distance between z1 and z2, it is equal to 
Aditya Gupta
2081 Points
4 years ago
From above
(Continued)
|12-8|
= 4 which is minimum value of the distance
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