My Math Forum Quadratic equations having complex numbers.

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 February 14th, 2017, 10:05 PM #1 Senior Member   Joined: Aug 2011 Posts: 534 Thanks: 2 Quadratic equations having complex numbers. Can we have Quadratic equations having complex numbers? Thanks & Regards, Prashant S Akerkar
 February 14th, 2017, 10:20 PM #2 Senior Member     Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus Sure. Consider $ix^2-(1+i)x+2=0$. It has solutions $\displaystyle x=\frac{\left( \sqrt{2}\,\sqrt{6}-2\right) i+\sqrt{2}\,\sqrt{6}+2}{4},x=-\frac{\left( \sqrt{2}\,\sqrt{6}+2\right) i+\sqrt{2}\,\sqrt{6}-2}{4}$.
February 14th, 2017, 10:27 PM   #3
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 Originally Posted by prashantakerkar 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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