Asked by tony
                 Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form.
[2(cos 240° + i sin 240°)]^5
            
        [2(cos 240° + i sin 240°)]^5
Answers
                    Answered by
            Count Iblis
            
    z = 2(cos 240° + i sin 240°) = 
2 exp(4/3 pi i)
z^5 = 2^5 exp(20/3 pi i) =
32 exp(2/3 pi i) =
-16 + 16 sqrt(3) i
    
2 exp(4/3 pi i)
z^5 = 2^5 exp(20/3 pi i) =
32 exp(2/3 pi i) =
-16 + 16 sqrt(3) i
                    Answered by
            Steve
            
    (2cis240°)^5 = 2^5 cis(5*240°)
= 32 cis1200°
= 32 cis120°
= -16 + 16√3 i
    
= 32 cis1200°
= 32 cis120°
= -16 + 16√3 i
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