- #1

cutecarebear

- 6

- 0

I'm having a bit of trouble with using the argument function with DeMoivres formula. I have the question:

**z**

^{8}= 16and am meant to find the solution using DeMoivre's formula (z

^{n}=r

^{n}(cosn(Θ) +isinn(Θ)) ). The problem is, I have no idea what an argument function is or how to find it. I've read around a bit and found that

**root(a**and that

^{2}+b^{2})= r**tan**

^{-1}(b/a) =argbut as you can see, I only have a (16) so that b=0, so is the argument then, tan

^{-1}(0)? I have several problems and they all have a but no b. However, in the answer section, they all have arguments. What the heck am I doing wrong?

## Homework Equations

I can do this one:

**z**as it has no argument (though I don't know why), and is just a matter of plugging in numbers.

^{3}=-1**z**

^{3}=-1z

^{3}=1(cos(Θ)+isin(Θ)

z=

_{3}√(1)(cos(Θ)+isin(Θ))

^{1/3}

z=1(cos(2kπ)+isin(2kπ)

^{1/3}

z=1(cos(2kπ/3)+isin(2kπ/3)

and then, since it has no argument, k can equal 0, +/-1, +/-2, +/-3 etc..., you plug in the k and solve.

## The Attempt at a Solution

I haven't gotten very far with this one

**z**

^{8}=16z

^{8}= 16

^{8}(cos8(Θ)+isin8(Θ)) or if I do it the other way

z=

_{8}√(16)(cos(2kπ)+isin(2kπ))

^{1/8}

z=

_{8}√(16)(cos(2kπ/8)+isin(2kπ/8))

and I can't insert anything for k, because I don't know the argument. I know I sound like a real novice at math (I am), but I hope someone can help me! Thank you so much in advance!