The largest value of r , for which the region represented by the set ω ∈ C ω - 4 - i ≤…

1. $2\sqrt{2}$
2. $\frac{3}{2}\sqrt{2}$
3. $\sqrt{17}$
4. $\frac{5}{2}\sqrt{2}$

Solution

$\left|z-1\right|\le \left|z+i\right|$
Putting $z=x+iy$ and simplifying, we get $x+y\ge 0$
The region in shown shaded right side of the line $x+y=0$



The largest value of $r$ would be the length of perpendicular from $A\left(4,1\right)$, on the line $x+y=0$

$\left|\frac{4+1}{\sqrt{2}}\right|= \frac{5}{\sqrt{2}}$$= \frac{5}{2}\sqrt{2}$ 

Asked in: JEE Main 2015 (10 Apr Online)

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