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Complex Numbers question

2021 · 26 Aug · Shift 2 · Q34

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JEE Main
Mathematics
Complex Numbers
2021 · 26 Aug · Shift 2 · Q34

Complex Numbers question

2021 · 26 Aug · Shift 2 · Q34

JEE MainMathematicsComplex NumbersMCQ+4 / −1

If

{\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)

, then p and q are roots of the equation :

A
${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$
B
${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$
C
${x^2} + \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$
D
${x^2} - \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$

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