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Complex Numbers question

2023 · 24 Jan · Shift 1 · Q24

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JEE Main
Mathematics
Complex Numbers
2023 · 24 Jan · Shift 1 · Q24

Complex Numbers question

2023 · 24 Jan · Shift 1 · Q24

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

\mathrm{p,q\in\mathbb{R}}

and

{\left( {1 - \sqrt 3 i} \right)^{200}} = {2^{199}}(p + iq),i = \sqrt { - 1}

then

\mathrm{p+q+q^2}

and

\mathrm{p-q+q^2}

are roots of the equation.

A
${x^2} + 4x - 1 = 0$
B
${x^2} - 4x + 1 = 0$
C
${x^2} + 4x + 1 = 0$
D
${x^2} - 4x - 1 = 0$

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