If ${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$, then p and q are roots of the equation :

Question

${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$

${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$

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

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

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