Real part

Definition and basic operations

For a complex number a + bi, the real number a is called its real part, and the real number b (not the complex number bi) is its imaginary part. The real part of a complex number z is denoted Re(z), ${\displaystyle {\mathcal {Re}}(z)}$, or ${\displaystyle {\mathfrak {R}}(z)}$; the imaginary part is Im(z), ${\displaystyle {\mathcal {Im}}(z)}$, or ${\displaystyle {\mathfrak {I}}(z)}$: for example, ${\textstyle \operatorname {Re} (2+3i)=2}$, ${\displaystyle \operatorname {Im} (2+3i)=3}$.