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(C) Given expression: $E = (\cos 2	heta + i\sin 2	heta )^{ - 5} (\cos 3	heta - i\sin 3	heta )^6 (\sin 	heta - i\cos 	heta )^3$. First,simplify t

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$i(\cos 25	heta - i\sin 25	heta )$

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(C) Given expression: $E = (\cos 2	heta + i\sin 2	heta )^{ - 5} (\cos 3	heta - i\sin 3	heta )^6 (\sin 	heta - i\cos 	heta )^3$. First,simplify the terms using De Moivre's Theorem: $(\cos 2	heta + i\sin 2	heta )^{ - 5} = \cos(-10	heta) + i\sin(-10	heta)$. $(\cos 3	heta - i\sin 3	heta )^6 = (\cos(-3	heta) + i\sin(-3	heta))^6 = \cos(-18	heta) + i\sin(-18	heta)$. $(\sin 	heta - i\cos 	heta )^3 = [-i(\cos 	heta + i\sin 	heta )]^3 = (-i)^3 (\cos 	heta + i\sin 	heta )^3 = i(\cos 3	heta + i\sin 3	heta)$. Multiplying these: $E = [\cos(-10	heta) + i\sin(-10	heta)] [\cos(-18	heta) + i\sin(-18	heta)] [i(\cos 3	heta + i\sin 3	heta)]$. $E = i [\cos(-10	heta - 18	heta + 3	heta) + i\sin(-10	heta - 18	heta + 3	heta)]$. $E = i [\cos(-25	heta) + i\sin(-25	heta)] = i(\cos 25	heta - i\sin 25	heta)$.

Express the following expression in the form $A + iB$: $(\cos 2\theta + i\sin 2\theta )^{ - 5} (\cos 3\theta - i\sin 3\theta )^6 (\sin \theta - i\cos \theta )^3$.

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