Simplifying a complex number divided by a real

Question

Is the equality

$$\frac{a+bi}{c} = \frac{a}{c}+\frac{b}{c}i$$

true for all real $a$, $b$ and $c \neq 0$ ?

Answer 1

Yes, that equation is true for all real $a, b$ and $c\ne0$.

Answer 2

The usual rules of arithmetic still apply in $\mathbb{C}$. Just about anything you can do in $\mathbb{R}$ you can do in $\mathbb{C}$.