JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(p , q \in R\) and \((1-\sqrt{3} i )^{200}=2^{199}( p + iq )\), \(i =\sqrt{-1}\) Then \(p + q + q ^2\) and \(p - q + q ^2\) are roots of the equation.
- A \(x ^2+4 x -1=0\)
- B \(x^2-4 x+1=0\)
- C \(x^2+4 x+1=0\)
- D \(x ^2-4 x -1=0\)
Answer & Solution
Correct Answer
(B) \(x^2-4 x+1=0\)
Step-by-step Solution
Detailed explanation
\((1-\sqrt{3} i )^{200}=2^{199}( p + iq )\) \(2^{200}\left(\cos \frac{\pi}{3}- i \sin \frac{\pi}{3}\right)^{200}=2^{199}( p + iq )\) \(2\left(-\frac{1}{2}- i \frac{\sqrt{3}}{2}\right)= p + iq\) \(p =-1, q =-\sqrt{3}\) \(\alpha= p + q + q ^2=2-\sqrt{3}\)…
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