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Question

If |Zi|2 and Z1=5+3i, then the maximum value of |iZ+Z1| is

A
7+13
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B
7+12
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C
7
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D
9
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Solution

The correct option is C 7
We have,
|Zi|2
Let z=x+iy, then
x2+(y1)24
So, Z lies on or inside the circle, whose center is (0,1) and radius is 2 units

Now,
|iZ+Z1|=|iZi2Z1|=|i(Zi(5+3i))|=|i||Z(3+5i)|=|Z(3+5i)| (|i|=1)

Point (3,5) lies outside the circle, so the maximum value of |iZ+Z1|
=(0+3)2+(15)2+2=7

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