how would you use demoivre's theorem to find (5(cos 3.2 + i sin 3.2))^4

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DeMoivre's theorem says that this is the same as(5^4)*(cos(4*3.2) + i*sin(4*3.2))= 625*(cos(12.8) + i*sin(12.8))~ 608.02 + i*144.69I don't know how your professor wants your solution, if he/she wants it exact, you should leave it with 625*cos(12.8) + i*625*sin(12.8), otherwise, just let him or her know that you rounded the real components to the second decimal place.