Complex Numbers 2 Question 47

48.

If z is any complex number satisfying |z32i|2, then the maximum value of |2z6+5i| is

(2011)

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Answer:

Correct Answer: 48. (5)

Solution:

  1. Given, |z32i|2

To find minimum of |2z6+5i|

or 2|z3+52i|, using triangle inequality

i.e. ||z1||z2|||z1+z2|

|z3+52i|=|z32i+2i+52i|

=|(z32i)+92i|

|z32i|92||292∣≥52

|z3+52i|52 or |2z6+5i|5



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