# Complex numbers | Exercises

Here I talked about complex numbers and introduced the Re and Im functions. In this post you can find exercises you can practice with to apply what you’ve learnt.

$5i+9-4i$ $\text{Re}\left&space;\{&space;5i^2&space;\right&space;\}$ $\text{Im}\left&space;\{&space;-5i^2&space;\right&space;\}$ $\text{Re}\left&space;\{&space;4i^2&space;+i\right&space;\}$ $\text{Im}\left&space;\{&space;4i^2&space;+i\right&space;\}$ $\text{Im}\left&space;\{&space;7+2i\right&space;\}$ $\text{Im}\left&space;\{&space;i\,&space;\text{Re}\left&space;\{&space;7+2i&space;\right&space;\}\right&space;\}$ $\text{Re}\left&space;\{&space;\varphi+\text{Im}\left&space;\{&space;7i\,&space;\text{Im}\left&space;\{&space;\pi&space;i\,&space;\text{Re}\left&space;\{&space;12-\text{Im}\left&space;\{&space;3+4i&space;\right&space;\}&space;\right&space;\}&space;\right&space;\}&space;\right&space;\}&space;\right&space;\}$ $\text{Im}\left&space;\{&space;\sqrt{\text{Re}\left&space;\{&space;24i^2+8i&space;\right&space;\}}&space;\right&space;\}$ $\text{Re}\left&space;\{&space;i\int&space;\sqrt{-x}&space;\,&space;dx\right&space;\}$ $\text{Im}\left&space;\{&space;\int&space;\left&space;(\frac{\sqrt{-x^2}&space;}{i}+\frac{x}{i}&space;\right&space;)\,&space;dx\right&space;\}$ $\text{Re}\left&space;\{&space;{\sqrt{\text{Re}\left&space;\{&space;\cos(\pi)+i\frac{\varphi\pi}{2}\sin(\ln(7))&space;\right&space;\}}}&space;\right&space;\}$ $\text{Im}\left&space;\{&space;\sqrt{-\varphi&space;i^2\int&space;i\sqrt{-8}\,&space;d\theta}&space;\right&space;\}$

You may find these links useful: