Hi, this is probably a really easy question but I'm kind of stuck.
Find the roots of x^4=16, and therefor find all four roots of y^4=-16.
I know that x = 2, 2i, -2, and -2i but I can not for the life of me find what y is.
Thanks!
y^4 = -16 All its roots are:
y = -2 (-1)^(1/4), y = 2 (-1)^(1/4), y = -2 (-1)^(3/4), y = 2 (-1)^(3/4)
Thanks. I’m sorry if this is too much to ask but could you explain why and how you got those answers?
Solve for y:
y^4 = -16
Take 4^th roots of both sides.
Taking 4^th roots gives 2 (-1)^(1/4) times the 4^th roots of unity:
y = -2 (-1)^(1/4) or y = 2 (-1)^(1/4) or y = -2 (-1)^(3/4) or y = 2 (-1)^(3/4)
