JEE Mains · Maths · STD 11 - 4.1 complex nubers
A complex number z is said to be unimodular if \(\left| z \right| = 1\) . Suppose \(z_1\) and \(z_2\) are complex number such that \(\frac{{{z_1} - 2{z_2}}}{{2 - {z_1}\overline {{z_2}} }}\) is unimodular and \(z_2\) is not unimodular . Then the point \(z_1\) lies on a:
- A Circle of radius \(\sqrt 2 \)
- B straight line parallel to \(x-\) axis
- C straight line parallel to \(y-\) axis
- D circle of radius \(2 \)
Answer & Solution
Correct Answer
(D) circle of radius \(2 \)
Step-by-step Solution
Detailed explanation
\(\left|\frac{z_{1}-2 z_{2}}{2-z_{1} \bar{z}_{2}}\right|=1\) \(\left|z_{1}-2 z_{2}\right|=\left|2-z_{1} \overline{z_{2}}\right|\) squaring both sides \(\left(z_{1}-2 z_{2}\right)(\overline{z_{1}}-2\)…
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