document.write( "Question 287649: Find all complex solutions of the equation $\"+x%5E4-x%5E3%2Bx%5E2-x=0+\"$ \n" ); document.write( "

Algebra.Com's Answer #208420 by CharlesG2(834) $\"\"$ $\"About$

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Find all complex solutions of the equation $\"+x%5E4-x%5E3%2Bx%5E2-x=0+\"$ \r
\n" ); document.write( "\n" ); document.write( "(moved from Algebra:Trigonometry-Basics to Algebra:Complex Numbers)\r
\n" ); document.write( "\n" ); document.write( "x^4 - x^3 + x^2 - x = 0
\n" ); document.write( "(x^2 + 1)(x^2 - x) = 0 (by FOIL x^4 - x^3 + x^2 - x = 0)
\n" ); document.write( "(x^2 + 1)(x - 1)x = 0
\n" ); document.write( "solutions: x = 0, x - 1 = 0, x^2 + 1 = 0\r
\n" ); document.write( "\n" ); document.write( "x - 1 = 0 --> x = 1\r
\n" ); document.write( "\n" ); document.write( "x^2 + 1 = 0 --> x^2 = -1 --> x = + - sqrt(-1) --> x = +- i\r
\n" ); document.write( "\n" ); document.write( "2 real solutions being: 0 and 1
\n" ); document.write( "2 complex solutions being: +- i which in complex form of a + bi would be written as 0 +- i
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