JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z\) is a complex number such that \(\frac{z-i}{z-1}\) is purely imaginary, then the minimum value of \(\mid \mathrm{z}-(3+3 \mathrm{i}) \mid\) is :
- A \(2 \sqrt{2}-1\)
- B \(3 \sqrt{2}\)
- C \(6 \sqrt{2}\)
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{z-i}{z-1}\) is purely Imaginary number Let \(z=x+\) iy \(\therefore \frac{x+i(y-1)}{(x-1)+i(y)} \times \frac{(x-1)-i y}{(x-1)-i y}\) \(\Rightarrow \frac{x(x-1)+y(y-1)+i(-y-x+1)}{(x-1)^{2}+y^{2}}\) is purely Imaginary number…
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