JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let for some real numbers \(\alpha\) and \(\beta\), a \(=\alpha-i \beta\). If the system of equations \(4 ix +(1+ i ) y =0\) and \(8\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right) x+\bar{a} y=0\) has more than one solution then \(\frac{\alpha}{\beta}\) is equal to
- A \(-2+\sqrt{3}\)
- B \(2-\sqrt{3}\)
- C \(2+\sqrt{3}\)
- D \(-2-\sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(2-\sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(a =\alpha- i \beta ; \alpha \in R ; \beta \in R\) \(4 ix +(1+ i ) y =0\) and \(8\left(\cos \frac{2 \pi}{3}+ i \sin \frac{2 \pi}{3}\right) x +\overline{ a } y =0\) \(\left|\begin{array}{cc}4 i \quad 1+ i \\ 8 e ^{ i 2 \pi / 3} \quad \overline{ a }\end{array}\right|=0\)…
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