Arithmetic's harmonics

So, $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ . $\frac{a+b}{ab}=\frac{1}{c}$ ; $a+b=c$ . a, b and c are not equal to 0, so we can multiply both sides by $(a+b)*(ab)$ $a^2 + 2ab + b^2 = ab$ ; $a^2 + ab + b^2 = 0$ ; $a=\frac{-b+-sqrt(b^2-4b^2)}{2}$ ); $a =$ $\frac{b}{2}$ +- $\frac{\sqrt{3}b}{2}$ i ; So, a, b and c must be complex numbers. $\boxed{C}$