This question looks streight forward but if someone could explain to me fully how to determine the solutions for this. It would help me understand it a lot. Thanks

For each of the following functions decide at which values of $\displaystyle z$ the function is continuous and at which values it is not continuous. Give reasons, but detailed proofs are not expected.

- $\displaystyle f(z)=5z^4+7z^3+3\overline z,$

- $\displaystyle f(z)=\frac{z-\overline z}{iz}.$ Check the cases i) $\displaystyle z\ne0,$ and ii) $\displaystyle z=0,$ separately.