Let $A[0 \ldots n-1]$ and $B[0 \ldots n-1]$ be two arrays containing $n$ real numbers such that $A[k] \leq A[k+1]$ and $B[k] \leq B[k+1]$ for all $k \in\{0,1, \ldots, n-2\}$. Design an efficient algorithm to find whether there exists any $k \in\{0,1, \ldots, n-1\}$ such that $A[k]+$ $i B[k]$, where $i=\sqrt{-1}$, forms a complex root of the equation $x^{2}+2 c x+c^{2}+d^{2}=0$ and $c$ and $d$ are real numbers. State and justify the time complexity of your algorithm.
