Find all the solutions to x^4+i=0. Write your answer in trig form.

(0 + i) + x^4 = 0

　

Subtract i from both sides:

x^4 = -i

　

Taking 4^th roots gives -(-1)^(7/8) times the 4^th roots of unity:

 

x = -(-1)^(3/8)    or    x = (-1)^(3/8)    or    x = -(-1)^(7/8)    or    x = (-1)^(7/8)