I have solved the roots of a quadratic equation and want to "test" them by putting them back in for x. I am having a problem with the x^2 term. Of the two roots, I'm only trying so far the positive square root case. I am trying to avoid writing all my work out since that would be hell and I also think would not be easy to read.(adsbygoogle = window.adsbygoogle || []).push({});

To evaluate x^2 where x = -2/3 + i√19, I first try the "from the ground up" method of just distributing, and eventually make a substitution of -1 for i^2. After making that substitution, I end up subtracting the term that had the i^2, from (9/4). After simplifying, I have (-5/2) + (-3i√19)/2

The second way I try to evaluate x^2 term is by using the multiplication definition of complex numbers (a + bi)(c + di) = (ac - bd) + (bc + ad)i . I find that (ac - bd) results in (9/4) - (19i^2)/4 and when I change i^2 to -1, now the terms are being added! Then when I add the (bc + ad)i part, I finally end up with (14/2) + (-3i√19)/2 .

Could someone point out the mistake here then? :S

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# Multiplying complex numbers

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