If \( (\sqrt{3} + i)^{100} = 2^{99}(p + iq) \), then \( p \) and \( q \) are roots of the equation:
\( x^2 - (\sqrt{3} - 1)x - \sqrt{3} = 0 \)
\( x^2 + (\sqrt{3} + 1)x + \sqrt{3} = 0 \)
\( x^2 - (\sqrt{3} + 1)x + \sqrt{3} = 0 \)
\( x^2 + (\sqrt{3} - 1)x - \sqrt{3} = 0 \)
