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The problem statement, all variables and given/known data

Let a, b and c be complex numbers with a not equal to 0. Show that the solution of [itex]az^2 + bz + c = 0[/itex] are [itex]z_1, z_2 = (-b \pm \sqrt(b^2 - 4ac))/(2a)[/itex]

The attempt at a solution

I'm assuming z is also complex. Multiplying the equation by 4ac and completing the square yields [itex](2az + b)^2 = b^2 - 4ac[/itex] There are two complex numbers, [itex]w_1, w_2[/itex], that are the square roots of [itex]b^2 - 4ac[/itex] so setting [itex]2az_j + b = w_j[/itex] and solving for [itex]z_j[/itex] yields

[tex]z_j = \frac{-b + w_j}{2a}[/tex]

for j = 1, 2. The section where I got this problem from does not define the square root of a complex numbers; it only talks about the roots of complex numbers. Would it be correct to stop here and consider the problem solved?

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# Homework Help: Complex Quadratic Formula

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