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Math Help - complex numbers equation

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    complex numbers equation

    how do you verify that i is a solution to z^4 -3z^3 -3z3z -4=0 and then find all other solutions?
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  2. #2
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    Quote Originally Posted by whatsyourquota View Post
    how do you verify that i is a solution to z^4 -3z^3 -3z3z -4=0 and then find all other solutions?
    You substitute z = i into the equation and show that it works.

    Then since all the coefficients of the equation are real, you know that z = -i is also a solution. So you know that (z - i)(z + i) = z^2 + 1 is a factor of z^4 - 3z^3 - 3z - 4.

    So factorise z^4 - 3z^3 - 3z - 4 as two quadratics. Then solve when the other quadratic is equal to zero.
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