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February 14th, 2017, 10:05 PM   #1
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Quadratic equations having complex numbers.

Can we have Quadratic equations having complex numbers?

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Prashant S Akerkar
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February 14th, 2017, 10:20 PM   #2
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Sure. Consider $ix^2-(1+i)x+2=0$. It has solutions $\displaystyle x=\frac{\left( \sqrt{2}\,\sqrt{6}-2\right) i+\sqrt{2}\,\sqrt{6}+2}{4},x=-\frac{\left( \sqrt{2}\,\sqrt{6}+2\right) i+\sqrt{2}\,\sqrt{6}-2}{4}$.
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February 14th, 2017, 10:27 PM   #3
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Quote:
Originally Posted by prashantakerkar View Post
Can we have Quadratic equations having complex numbers?

Thanks & Regards,
Prashant S Akerkar
You do lose the property that the roots are either real or complex conjugates of one another.
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