document.write( "Question 204120: How did they come up with the quadratic formula x=-b+ b^s-4AC/2A? and what is the purpose of imaginary numbers such as -1 and i? I don't have a square root symbol so the negative 1 is to have a sqrt. sympbol and also for the problem for the quadratic formula. Thank you you knowledge is very appreciated!!!!
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #154073 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Well there's a long derivation to find the quadratic formula (which I'm sure that it will take a while to type up), but you can find a derivation here.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As for $\"sqrt%28-1%29\"$ and \"i\", it turns out that $\"sqrt%28-1%29\"$ comes up pretty often that mathematicians and all of their laziness decided to call \"i\" the $\"sqrt%28-1%29\"$ . So this means that $\"i=sqrt%28-1%29\"$ . So when we say $\"2%2B3i\"$ we really mean $\"2%2B3%2Asqrt%28-1%29\"$ . This notation saves a lot of time writing and helps with calculations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As for why imaginary numbers are useful, you probably need to be a little more patient. There are a number of applications in physics (such as electrical engineering) that imaginary and complex numbers are useful in. I honestly cannot tell you which ones specifically as I'm not an engineer. I'm pretty sure that there are other uses, I just can't think of them right now. \n" ); document.write( "

\n" );