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

 Mar 12, 2018
 #1
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(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)

 Mar 13, 2018

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