Question 1085721
<font color="black" face="times" size="3">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 = <font color=red>-40.5 - 70.148025i</font>
The result is approximate.</font>