How do you find all the complex roots of $x^3-x^2+x-1$ ?

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Answer 1 · 2016-02-19T19:37:49

$x = 1 , i , -i$

Step 1: Set the equation to equal to zero

$x^3-x^2+x-1= 0$

Step 2: Group the terms like this

$color (red)((x^3-x^2)) + color(blue)((x-1)) = 0$

Step 3: Factor out the common like term for each group

$x^2color(red)((x-1)) + 1color(red)((x-1)) = 0$
$(x^2 +1)(x-1) = 0$

Step 4 Set each factor equal to zero

$x^2 +1" " = 0$
$" " -1 " " " " -1$
$x^2" " " = " " -1$
$sqrt(x^2) " " = sqrt(-1)$

$x = +- i$

or

$x-1= 0$
$x = 1$

Answer: $x = 1 , i , -i$

How do you find all the complex roots of x^3-x^2+x-1x^3-x^2+x-1?