The [[Complex Numbers|Complex]] [[Plane]] is the shorthand for referring to the two-dimensional [[Plane]] / [[Vector Space]] [[Span|spanned]] by the [[Basis Vectors]] $1$ and $i$. When discussing the complex plane, typically the $i$-axis is represented up and down while the [[Real Numbers|Real]] [[Axis]] is measured left to right as if it were an extension of the [[Real Number Line]].