Real and Imaginary Parts of a Complex Number

In the setting of The Complex Numbers, with the Real Numbers Identified with a Subset of the Complex Numbers, let $z\in\mathbb{C}$.

¶ The real part $\operatorname{Re}z$ and the imaginary part $\operatorname{Im}z$ of $z$ are the real numbers $a$ and $b$, respectively, with $z=a+bi$; such $a$ and $b$ exist and are unique by The Complex Numbers, with the Real Numbers Identified with a Subset of the Complex Numbers §canonical.