SOLUTION: Solve: X^4 + 100 = 0 The problem is that the students only have factoring, irrational, and complex numbers as their background. Let a = x^2 a^2 = -50 a = 5i*{sqrt(2)}

Question 663690: Solve:
X^4 + 100 = 0
The problem is that the students only have factoring, irrational, and complex numbers as their background.
Let a = x^2
a^2 = -50
a = 5i*{sqrt(2)}
x^2 = 5i*{sqrt(2)}
How to find x?
Use synthetic division and guess? That doesn't seem to work too well either?
Recommendations for new Algebra II students? Thanks.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve:
X^4 + 100 = 0
-----------------

Use DeMoivre's Theorem
x^4 = 100cis(180) + n*360
x = sqrt(10)cis(45) + n*90
x = sqrt(10)cis(45), ...cis(135), cis(225), cis(315)
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Probably more than Algebra 2 can do, tho.
--> not an appropriate problem for Algebra 2.

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