JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z =1+ i\) and \(z _1=\frac{1+ i \overline{ z }}{\overline{ z }(1- z )+\frac{1}{ z }}\). Then \(\frac{12}{\pi}\) \(\arg \left(z_1\right)\) is equal to \(..........\).
- A \(18\)
- B \(27\)
- C \(36\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
\(z=1+i\) \(z_1=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}\) \(z_1=\frac{1+i(1-i)}{(1-i)(1-1-i)+\frac{1}{1+i}}\) \(=\frac{1+i-i^2}{(1-i)(-i)+\frac{1-i}{2}}\) \(=\frac{2+i}{-3 i-1}=\frac{4+2 i}{-3 i-1}\) \(=\frac{-(4+2 i)(3 i-1)}{(3 i)^2-(1)^2}\)…
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