JEE Mains · Maths · STD 11 - 4.1 complex nubers
If the set \(\left\{\operatorname{Re}\left(\frac{z-\bar{z}+z \bar{z}}{2-3 z+5 \bar{z}}\right): z \in C , \operatorname{Re}(z)=3\right\}\) is equal to the interval \((\alpha, \beta]\), then \(24(\beta-\alpha)\) is equal to
- A \(36\)
- B \(42\)
- C \(27\)
- D \(30\)
Answer & Solution
Correct Answer
(D) \(30\)
Step-by-step Solution
Detailed explanation
Let \(z_1=\left(\frac{z-\bar{z}+z \bar{z}}{2-3 z+5 \bar{z}}\right)\) Let \(z=3+i y\) \(\bar{z}=3-i y\) \(z_1=\frac{2 i y+\left(9+y^2\right)}{2-3(3+i y)+5(3-i y)}\) \(=\frac{9+y^2+i(2 y)}{8-8 i y}\) \(=\frac{\left(9+y^2\right)+i(2 y)}{8(1-i y)}\)…
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