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

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) (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.
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