Question

What is the forth root of -4 in trigonometric form?

Answer 1

\[\Large\rm (-4)^{1/4}=\left(-4+0\mathcal i\right)^{1/4}\]Mmmmm what methods have you learned for solving problems like this?
Are you familiar with De Moivre's Theorem?

Answer 2

Putting it into exponential form first might be easier. hmm
whatchu think? :)

Answer 3

Yes i am familiar with De Moivre's theorem and that is what we need to put it into is that what your answer is in?

Answer 4

Ummm I guess maybe we should first separate the -1 and 4.\[\Large\rm (-4)^{1/4}=4^{1/4}\cdot (-1)^{1/4}=\sqrt2\cdot (-1)^{1/4}\]\[\Large\rm =\sqrt2\cdot (-1+0\mathcal i)^{1/4}\]
Relating these two terms to our sine and cosine,\[\Large\rm \cos \theta=-1, \qquad\qquad\qquad \sin \theta=0\]What value do we get for theta? :)

Answer 5

There are many ways to approach a problem like this one, hopefully I'm doing it in a way that makes sense to you..

Answer 6

we are suppose to use this form to find the answer… Use the formula De Moivre's theorem to find the indicated roots of the complex number. (Enter your answers in trigonometric form. Let 0 ≤ θ < 2π.). Does this help with my question?

Answer 7

Ok so we're using De Moivre's.
But before we can do that, we have to have a trigonometric form first.

See how we have just a number?
We need to get it written in terms of sine and cosine before we can apply De Moivre's Theorem. This is the tricky part.

Answer 8

I was trying to do some algebra to simplify it down first, but maybe that's making it more confusing for you.

Answer 9

Umm maybe this is easier.. it still requires a little algebra, but not as much to start.\[\Large\rm \left[4\color{orangered}{(-1)}\right]^{1/4}\]So I split up the 4 and -1.
Let's pay attention to this orange part first, we want to try and write it in trig form.