Question

Find all the solutions of the equation. Leave answers in trigonometric form.
X^4 + 625 = 0

Answer 1

@Koikkara
@johnweldon1993

Answer 2

First lets right this in a better from, no?

x^4 = -625

Answer 3

We want to find all the trigonometric roots, correct?

Answer 4

yes

Answer 5

For instance
x^3 - 27 = 0
so we got r=3
but for this idk how we get r....

Answer 6

im thinking hmmm...
I believe...

-625 = 625(cos(pi(1 + 2k)) + i sin(pi(1 + 2k))) (thinking more... I truly hate trig sometimes)

Answer 7

The number 27 is the solution for
x^3 - 27= 0

Answer 8

i meant 28

Answer 9

but for -625 idk how to get r

Answer 10

Oh oh, converting to i like that was silly.
Just change -1 to sines and cosines, maybe that will make more sense.\[\Large\rm x=\sqrt[4]{-625}\]\[\Large\rm x=\pm 5 \sqrt[4]{\color{orangered}{-1}}\]So we can rewrite our -1 in terms of sine and cosine,\[\Large\rm x=\pm 5 \sqrt[4]{\color{orangered}{\cos \pi+\mathcal i \sin \pi}}\]