For all complex numbers z1, z2 satisfying |z1|=12 And |z2-3-4i|=5 , then minimum value of lz1-z2l =is .....
For all complex numbers z1, z2 satisfying |z1|=12 And |z2-3-4i|=5 , then minimum value of lz1-z2l =is .....
User , 7 Years ago
Grade
Algebra> For all complex numbers z1, z2 satisfying...
2 Answers
Arun
Dear student
If we analyse it geometrically then,
| z1| = 12 means
Locus of all points which has centre at (0,0) and at a distance of 12 units i.e. a circle of radius 12 units.
| z2 - 3 - 4i | = 5
Means
Locus of points which are at a dostance of 5 units from a fixed point (3,4)
Hence minimum value of |z1-z2| = 12 - 10 = 2 units
Regards
Arun (askIITians forum expert)
Pranjal Srivastava
|z2-3-4i -z1 +z1|=5
for minimum value, 5>|Iz2-z1I – Iz1-3-4iI|
therefore, 5>|z1-z2| – |z1| – |3+4i|
So, |z1-z2|
the minimum value of |z1-z2| is 22.
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