# Complex Numbers Real and Imaginary parts

Ιf I have a $Z_n= (n^2+in)/(n^2 +1)$ am I right to assume that the real part is $n^2/(n^2 +1)$ and the imaginary part is $in/(n^2+1)$ it seems to simple to be that

• to ass${{{{}}}}$? – Lord Shark the Unknown Oct 14 '17 at 15:01
• assume @LordSharktheUnknown – MCCCS Oct 14 '17 at 15:03
• Sorry I meant assume – Rich Oct 14 '17 at 15:03
• If $a$ and $b$ are real, then $b$ is the imaginary part of $a+ib$. – Lord Shark the Unknown Oct 14 '17 at 15:05
• Only, if $n$ is real. If $n$ is complex, you have more work to do. – Laray Oct 14 '17 at 15:06

Yes you can. $$Z_n = \frac{n^2 +in}{n^2+1}= \frac{n^2}{n^2 +1} + \frac{n}{n^2 +1} i$$ So the real part is $\frac{n^2}{n^2 +1}$ and the imaginary is $\frac{n}{n^2 +1}$ (without the $i$).