Ok guys, I'm back! This is gonna be my last question here, as I have practically finished test review.
Raise to the the power:
b ) $(8 cis(120 ^\circ)))^{1/3}$
... Well for this there are two formulas available.. I'm asking which one am I suppose to use for this equation?
1) $z^n = r^n * cos(n*\Theta)$
$x^{1/n} = r^{1/n}\frac{1}{n} \cdot \Theta + \frac{1}{n} \cdot 360k$
2) So I just decided to use first one.. and did:
$8^{1/3} cis(\frac{1}{3} \cdot 120^\circ)$
$2cis(40)$
But the answers are:
$$2cis(40^\circ) , 2cis(160^\circ), 2cis(280^\circ)$$
You should have used the second one.
Both of these formulae assume that $n$ is an integer, which means you can't plug in $n=1/3$ into the first equation. But you can plug in $n=3$ into the second equation.
(The only case when the two formulas could both be used is when raising to the power 1. You should check that you do get the same answer regardless of which formula you use.)
[Actually, the "right" answer is that both formulae work for $n$ not an integer as well, but you will generally get different answers; there is a reason for this but it is not so simple to explain. Based on the way that the answer is formatted, it seems that they want you to consider the integer case only.]