SOLUTION: Find all complex solutions of the equation {{{ x^4-x^3+x^2-x=0 }}}
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Question 287649: Find all complex solutions of the equation
Found 2 solutions by richwmiller, CharlesG2:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
How is this trig?
Factor out x to begin.
x*(x^3-x^2-x-1)=0
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Find all complex solutions of the equation
(moved from Algebra:Trigonometry-Basics to Algebra:Complex Numbers)
x^4 - x^3 + x^2 - x = 0
(x^2 + 1)(x^2 - x) = 0 (by FOIL x^4 - x^3 + x^2 - x = 0)
(x^2 + 1)(x - 1)x = 0
solutions: x = 0, x - 1 = 0, x^2 + 1 = 0
x - 1 = 0 --> x = 1
x^2 + 1 = 0 --> x^2 = -1 --> x = + - sqrt(-1) --> x = +- i
2 real solutions being: 0 and 1
2 complex solutions being: +- i which in complex form of a + bi would be written as 0 +- i
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