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if |z-i| less than equal to 2. (z1)=5+3i, then the maximum value of |iz+z1| is (z and z1 are complex no.).

if |z-i| less than equal to 2. (z1)=5+3i, then the maximum value of |iz+z1| is (z and z1 are complex no.).
 
 

Grade:11

3 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
Solution in the figure
512-2188_sol3.jpg
jagdish singh singh
173 Points
8 years ago
\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 $\max|iz+z`| = 7$
SREEKANTH
85 Points
7 years ago
if you take  z=x+iy
|z-i|=sqrt(x^2+(y-1)^2)
         x^2+(y-1)^2
         x^2+y^2-2y
z1=5+i3
the maximum value of |iz+z1|=|ix-y+5+i3|
                                                  =|(5-y)+i(x+3)|
                                                  =sqrt(5-y)^2+(x+3)^2)
                                                  =sqrt(x^2+y^2+6x+34-10y)
                                                  =sqrt(1.99+34+6x-8y)
                                                  =sqrt(1.99+34+6(0.9)-8(0.9)
                                                 =sqrt(34+7.3-7.2)
                                           s0  maximum value sqrt(34.111)
 

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