What is the Use of deMoivre's Formula in Finding Roots of Complex Numbers?

[mohamen]

wat is under root - i ?

please anser this

 

[Hurkyl]

Do you mean $\sqrt{-i}$? You can figure it out yourself! If $a + bi = \sqrt{-i}$, then what does the definition of square root tell you?

 

[dextercioby]

HINT:

$$-i=e^{-\frac{i\pi}{2}+2k\pi} , \ k\in\mathbb{Z}$$

Daniel.

 

[Gib Z]

Hey guys, don't post here often, i will more from now on. Anyway, dexter got that from the identity e^(ix)= cos x + i sin x.

 

[mohamen]

will it be solved by the de mouvies theorm...i don't think so...

 

[dextercioby]

You mean "de Moivre". Yes, it will, since that theorem is a trivial consequence of the fact that

$$\left(e^{ix}\right)^{n}=e^{inx}$$

Daniel.

 

[HallsofIvy]

will it be solved by the de mouvies theorm...i don't think so...

I personally like Hurkyl's suggestion best but WHY don't you think deMoivre's formula will work? It can be used to find any root of any complex number.