SOLUTION: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. 3(cos(150°) + i sin(150°))^4 please help me solve this

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Question 1085721: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
3(cos(150°) + i sin(150°))^4


please help me solve this
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z = 3(cos(150°) + i sin(150°))

We want to find z^4. Raise both sides of the initial equation to the 4th power.
Then use De Moivre's Theorem to get...

z = 3(cos(150°) + i sin(150°))
z^4 = [3(cos(150°) + i sin(150°))]^4
z^4 = (3^4)*(cos(4*150°) + i sin(4*150°))
z^4 = 81*(cos(600°) + i sin(600°))
z^4 = 81*(-0.5 + i*(-0.866025))
z^4 = 81*(-0.5) + 81*i*(-0.866025)
z^4 = -40.5 - 70.148025i
The result is approximate.