JEE Mains · Maths · STD 11 - 4.1 complex nubers
If the least and the largest real values of \(\alpha,\) for which the equation \(z+\alpha|z-1|+2 i=0\) \(( z \in C\) and \(i=\sqrt{-1}\) ) has a solution, are \(p\) and \(q\) respectively; then \(4\left( p ^{2}+ q ^{2}\right)\) is equal to ..........
- A \(15\)
- B \(10\)
- C \(20\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(10\)
Step-by-step Solution
Detailed explanation
Put \(z=x+\) iy \(x+i y+\alpha \mid x+\) iy \(-1 \mid+2 i=0\) \(\Rightarrow \quad x+\alpha \sqrt{(x-1)^{2}+y^{2}}+i(y+2)=0+0 i\) \(\Rightarrow \quad y+2=0\) and \(x+\alpha \sqrt{(x-1)^{2}+y^{2}}=0\) \(\Rightarrow \quad y=-2\) and \(\alpha^{2}=\frac{x^{2}}{x^{2}-2 x+5}\) Now…
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