Complex numbers/Real and imaginary part/Definition

For a complex number

${\displaystyle {}z=a+b{\mathrm {i} }\,,}$

we call

${\displaystyle {}\operatorname {Re} \,{\left(z\right)}=a\,}$

the real part of ${\displaystyle {}z}$ and

${\displaystyle {}\operatorname {Im} \,{\left(z\right)}=b\,}$

the imaginary part of ${\displaystyle {}z}$.