Consider the equation
$$\frac{1}{a} + \frac{1}{b} = \frac{1}{a+b}$$
Choose the correct statement(s) from below:\\
(A) There exists $(a,b) \in \mathbb{R}^2$ satisfying the above equation;\\
(B) There exists $(a,b) \in \mathbb{C}^2$ satisfying the above equation;\\
(C) There exists $(a,b) \in \mathbb{C}^2$ with $a = b$ satisfying the above equation;\\
(D) There exists $(a,b) \in (\mathbb{F}_3)^2$ with $a = b$ satisfying the above equation.