Cartesian form of a complex number

A complex number \(z\) when represented in the form \(x+yi\) is said to be in Cartesian form.

A complex number \(z\) is said to be purely imaginary if \(\mathrm{Re}(z)=0\), i.e., its real part is zero.

Any real number \(x\) and the complex number \(x+0i\) are one and the same entity, i.e., \(x+0i=x\).

Whence a complex number \(z\) is a real number if and only if \(\mathrm{Im}(z)=0\).