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Question

If |z+2i|=5, then the maximum value of |3z+97i| is
  1. 15
  2. 20
  3. 5
  4. 10


Solution

The correct option is B 20
Given,
|z+2i|=5(i)

Now, |3z+97i|=|3z+63i+34i|

We know that,
|z1+z2||z1|+|z2|
|3z+63i+34i||3z+63i|+|34i||3z+97i|3|z+2i|+|34i|
|3z+97i|3(5)+5  [from (i)]
|3z+97i|20

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