Express the following in $a+ib$ form:
(i) ${\left(\frac{\cos \theta +i\sin \theta }{\sin \theta +i\cos \theta }\right)}^4$
(ii)$\frac{{\left(\cos 2\theta -i\sin 2\theta \right)}^4{\left(\cos 4\theta +i\sin 4\theta \right)}^{-5}}{{\left(\cos 3\theta +i\sin 3\theta \right)}^{-2}{\left(\cos 3\theta -i\sin 3\theta \right)}^{-9}}$
(iii) $\frac{{\left(\sin \pi /8+i\cos \pi /8\right)}^8}{{\left(\sin \pi /8-i\cos \pi /8\right)}^8}$

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