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Question

For all complex numbers z1,z2 satisfying |z1|=12and|z234i| = 5, the minimum value of |z1z2| is
[IIT Screening 2002]
  1. 17
  2. 0

  3. 2

  4. 7


Solution

The correct option is C

2


The two circles are C1(0,0),r1=12,C2(3,4),r2=5 and it passes through origin, the centre of C1.
C1C2=5<r1r2=7


Hence circle C2 lies inside circle C1.

Therefore minimum distance between them is AB=C1B=C1A=r12r2=1210=2.

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