Complex numbers/Real and imaginary part/Definition

Real part, imaginary part

For a complex number

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

we call

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

the real part of ${}z$ and

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

the imaginary part of ${}z$.