#math/linear-algebra Suppose $z=a+bi$, where $a$ and $b$ are real numbers. `real component` of $z$ is defined by $\text{Re }z=a$. Similarly, the `imaginary component` of $z$ is defined by $\text{Im }z=b$. Thus, we have $z=\text{Re }z+(\text{Im }z)i$. ## Complex Conjugate $\Huge{\bar{z}}$ The `complex conjugate` of $z\in \mathbf{C}$, denoted by $\bar{z}$, is defined by $\bar{z}=\text{Re }z-(\text{Im }z)i.$ The `absolute value` of a complex number $z$, denoted by $\lvert z \rvert$, is defined by $ \lvert z \rvert =\sqrt{(\text{Re z})^{2}+(\text{Im }z)^{2}}. $