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|z – i| is less than or equal to 2 and z2 = 5+3i , then the maximum value of |iz+ z2| is a) 2+sqrt(31) b)7 ​c) sqrt(31) – 2 d)none of these

|z – i| is less than or equal to 2 and z2 = 5+3i , then the maximum value of |iz+ z2| is 
a) 2+sqrt(31)
b)7
​c) sqrt(31) – 2
d)none of these

Grade:

1 Answers

Arun
25750 Points
5 years ago
Dear Meghendra
 
\hspace{-18}$Given $|z-i|\leq 2$ and $z` = 5+3i\;,$ Then we calculate $\max|iz+z`|$\\\\\ So $|iz+z`| = |i(z-i)+4+3i|\leq |i(z-i)|+|4+3i|\leq |i||z-i|+5$\\\\So we get $|iz+z`|\leq |z-i|+5=2+5=7$\\\\So we get $\max|iz+z`| = 7$
 
 
Hope it helps
 
In case iof any query please feel free to ask.
 
Regards
Arun (askIITians forum expert)

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