If z is a complex number such that (z-i)/(z-1) is purely imaginary, then the minimum value of |z-(3+3i)| is :

Complex Numbers: If z is a complex number such that (z-i)/(z-1) is purely imaginary,… | JEE Main 2021

JEE Main 2021 (Online) 31st August Evening ShiftQuestion 1

If $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary, then the minimum value of $|z-(3+3i)|$ is :

Complex Numbers

$2\sqrt{2}-1$$2\sqrt{2}$✓ Correct answer$3\sqrt{2}$$6\sqrt{2}$

Solution

$\frac{z-i}{z-1}$ purely imaginary $\Rightarrow$ $z$ lies on the circle with diameter joining $1$ and $i$: centre $(\frac12,\frac12)$, radius $\frac{\sqrt2}{2}$. Distance from $(3,3)$ to centre $=\frac{5\sqrt2}{2}$. Min $=\frac{5\sqrt2}{2}-\frac{\sqrt2}{2}=2\sqrt2$. Option (B).

Complex Numbers - JEE Mathematics question (JEE Main 2021 (Online) 31st August Evening Shift)

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