Question

how do i get -100000 into polar form to find all 5 complex 5th roots?

Answer 1

(-10)^5=-100000

Answer 2

yeah i know but i need to show all the work using demoivres theorem

Answer 3

so i need to get it into polar form....like cos sin

Answer 4

\[x^5=-100000\] so that's the question right?

Answer 5

and now you want to use laws of demoivre to get all the answer in form of polar coordinates?

Answer 6

Find all the COMPLEX FIFTH ROOTS OF -100000. Write the roots in rectangular form.

Answer 7

well so I guess my equation above is correct, excuse me, my english is not flawless but that's what I would do, because the equation above has 5 roots in the complex plane. So you can tell already from the equation above, that this can be written as:

\[x^5=-100000 +0i \] which means it is located on the negative real axis, therefore an argument of this can be found, an argument is \(\pi\)

Answer 8

im looking for 5 roots...five different answers.

Answer 9

\[ \phi = \frac{\pi}{5} + \frac{2\pi k }{5} \]
k \( \in \mathbb{N}\)

Answer 10

gives you five answer, choose k=0, k=1, k=2, K=3, k=4

Answer 11

what is k

Answer 12

i have no idea where that comes from im just going to have to do this myself. thanks anyways.

Answer 13

a number, you can choose it for yourself, just like in trigonometry when you are looking for all the various angles that satisfy an equation.

Answer 14

well it's the legit way, what you are looking for is the following

\[ \sqrt[5]{100000}( \text{cis} \phi) \]

Answer 15

this is the polar coordinate form, the result can be both, either polar or rectangular.

Answer 16

\[ 10 ( \cos \phi + i\sin \phi) \]

Answer 17

ive got it.

Answer 18

good (-: