De Moivre's Theorem

1. Jan 1, 2010

Wardlaw

1. The problem statement, all variables and given/known data

Using De Moivres Theorem, solve (-12-5i)^-3

2. Relevant equations

3. The attempt at a solution

The solution i get for this problem is different from the one given in the exercise text. This is 1/2197cis(8.241)

Note: cis is equivalent to cos($$\Theta$$)+isin($$\Theta$$)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 1, 2010

latentcorpse

well you haven't actually written an equation down so there's nothing to solve.
i'm assuming you meant to rewrite it in polar form and then use de moivre

write -12-5i in polar form, that is z=r cis(theta)
where r will be 13 if my mental pythagoras is correct and theta is arctan(y/x)

then use de moivre (-12-5i)^(-3)=z^(-3)=r^(-3) cis(-3 theta)

3. Jan 1, 2010

kbaumen

Remember that in the Argand diagram,-12-5i lies in the 3rd quadrant. Thus

$$\theta = tan^{-1}(y/x) - \pi$$