JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(w\) \((Im\, w \neq 0)\) be a complex number. Then the set of all complex number \(z\) satisfying the equation \(w - \overline {w}z = k\left( {1 - z} \right)\) , for some real number \(k\), is
- A \(\left\{ {z:\left| z \right| = 1} \right\}\)
- B \(\left\{ {z:z = \overline z } \right\}\)
- C \(\left\{ {z:z \ne 1} \right\}\)
- D \(\left\{ {z:\left| z \right| = 1,z \ne 1} \right\}\)
Answer & Solution
Correct Answer
(D) \(\left\{ {z:\left| z \right| = 1,z \ne 1} \right\}\)
Step-by-step Solution
Detailed explanation
Consider the equation \(w-\bar{w} z=k(1-z), k \in R\) Clearly \(z \neq 1\) and \(\frac{w-\bar{w} z}{1-z}\) is purely real \(\therefore \frac{\overline{w-\bar{w} z}}{1-z}=\frac{w-\bar{w} z}{1-z}\) \(\Rightarrow \frac{\bar{w}-w \bar{z}}{1-\bar{z}}=\frac{w-\bar{w} z}{1-z}\)…
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