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Basic Concepts
Definition: $i=\sqrt{-1}$
Complex number: $a+bi$, where $a$ is real part，$bi$ is imaginary part. $a={\rm Re}(\mathbb{Z})$, $b={\rm Im}(\mathbb{Z})$
Notes: $i^2=-1$, $i^3=-i$, $i^4=1$
It can also be written in vector form, such as $a \choose b$ (Note: this writing is only useful when calculating addition and subtraction, other operations are more troublesome).