Question

What are all the roots for r^4+1=0 and how do I find them?

Answer 1

A root is anywhere where a function is equal to zero. Your equation equals zero when:
\[r^4 = -1\]
Which has no real roots.

Answer 2

What are the non real roots

Answer 3

Have you covered complex numbers? Are you expected to give the complex roots?

Answer 4

yeah

Answer 5

\[r^4=\cos(\pi+2n \pi)+i \sin(\pi+2n \pi)\]
since cos(pi)=-1 and sin(pi)=0
the right hand side is still -1
since -1+0=-1

Answer 6

use demoirve's law (i think that is what it is called)

Answer 7

The solution shows me radical2/2 +/- radical2/2 i; -rdicL2/2 =/- radical 2/2 i @myininaya but I'm not sure how to get those

Answer 8

take the 4 root of both sides

Answer 9

ohh right thank youuu!

Answer 10

you would have one solution given by n=0
another by n=1
another by n=2
and the last by n=3

Answer 11

that is 4 solutions