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