SOLUTION: x^4= 16 using complex numbers solve for x. couldn't find any examples like this in the book. i get the same answer every time : 2, -2 yet the back of the book has -2i and 2i a

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: x^4= 16 using complex numbers solve for x. couldn't find any examples like this in the book. i get the same answer every time : 2, -2 yet the back of the book has -2i and 2i a      Log On


   

Question 495037: x^4= 16
using complex numbers solve for x. couldn't find any examples like this in the book.
i get the same answer every time : 2, -2 yet the back of the book has -2i and 2i also.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+=+16
x%5E4+-+16+=+0
%28x%5E2-4%29%2A%28x%5E2%2B4%29+=+0
x%5E2-4+=+0
x = -2, +2
----------
x%5E2%2B4+=+0
x%5E2+=+-4
x = -2i, +2i
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The number of roots = the order of the equation.
4th order --> 4 roots
Sometimes the roots are repeated, eg, x^3=0
--> x = 0,0,0
3 roots, of 0, multiplicity 3