(a) Find \(a\) and \(b\) such that
\[z^{8}-\mathrm{i} z^{5}-z^{3}+\mathrm{i}=\left(z^{5}-a\right)\left(z^{3}-b\right) .\]
(b) Hence find the roots of
\[z^{8}-\mathrm{i} z^{5}-z^{3}+\mathrm{i}=0\]
giving your answers in the form \(r \mathrm{e}^{\mathrm{i} \theta}\), where \(r>0\) and \(0 \leqslant \theta<2 \pi\).