A sequence \left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right),\left(a_{3}, b_{3}\right), \ldots of points in the coordinate plane satisfies
\left(a_{n+1}, b_{n+1}\right)=\left(\sqrt{3} a_{n}-b_{n}, \sqrt{3} b_{n}+a_{n}\right) \quad \text { for } \quad n=1,2,3, \ldots
Suppose that \left(a_{100}, b_{100}\right)=(2,4). What is a_{1}+b_{1} ?
Answer Choices
A. -\dfrac{1}{2^{97}}
B. -\dfrac{1}{2^{99}}
C. 0
D. \dfrac{1}{2^{98}}
E. \dfrac{1}{2^{96}}