Question
Question: For all complex numbers z<sub>1</sub>, z<sub>2</sub> satisfying \|z<sub>1</sub>\| = 12 and \|z<sub>...
For all complex numbers z1, z2 satisfying |z1| = 12 and
|z2 – 3 – 4i| = 5, the minimum value of |z1 – z2| is –
A
0
B
2
C
7
D
17
Answer
2
Explanation
Solution
Sol. \ |z1 – z2| ³ ||z1| – |z2||
\ |z2 – 3 – 4i| ³ ||z2| – |3 + 4i|| Ž 5 ³ ||z2| – 5|
Ž – 5 £ |z2| –5 £ 5
Ž |z2| £ 10 Ž – |z2| ³ –10
\ |z1| – |z2| ³ 12 – 10 = 2
But |z1 – z2| ³ |z1| – |z2| ³ 2 Ž Minimum value of |z1 – z2| is 2.