document.write( "Question 1053141: Find an nth degree polynomial function with real coefficients satisfying the given conditions.
\n" ); document.write( "n=3; -4 and 6+5i are zeros; f(1)=250
\n" ); document.write( "My question is not exactly the answer to this problem. My question is what are 'i's, referring to 6+5i, and how they affect the entire problem. \n" ); document.write( "

Algebra.Com's Answer #668388 by ikleyn(52927) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find an nth degree polynomial function with real coefficients satisfying the given conditions.
\n" ); document.write( "n=3; -4 and 6+5i are zeros; f(1)=250
\n" ); document.write( "My question is not exactly the answer to this problem. My question is what are 'i's, referring to 6+5i, and how they affect the entire problem.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1.  6+5i is the complex number.\r\n" );
document.write( "    6 is its real part.\r\n" );
document.write( "    5i is its imaginary part.\r\n" );
document.write( "    i is that famous complex number (\"imaginary unit\") which is  = -1.\r\n" );
document.write( "\r\n" );
document.write( "2.  The polynomials with real coefficients all have this remarkable property:\r\n" );
document.write( "    if  a+bi is the root of such a polynomial, then the so named (so called) conjugate complex number a-bi is the complex root also.\r\n" );
document.write( "\r\n" );
document.write( "3.  Since you ask such a question (of an introductory level), then I think \r\n" );
document.write( "    it might be useful for you to make acquaintance with complex numbers.\r\n" );
document.write( "\r\n" );
document.write( "    You may use the lessons in this site:\r\n" );
document.write( "\r\n" );
document.write( "        - Complex numbers and arithmetic operations on them\r\n" );
document.write( "\r\n" );
document.write( "        - Complex plane\r\n" );
document.write( "\r\n" );
document.write( "        - Addition and subtraction of complex numbers in complex plane\r\n" );
document.write( "\r\n" );
document.write( "        - Multiplication and division of complex numbers in complex plane\r\n" );
document.write( "\r\n" );
document.write( "        - Raising a complex number to an integer power\r\n" );
document.write( "\r\n" );
document.write( "        - How to take a root of a complex number\r\n" );
document.write( "\r\n" );
document.write( "        - Solution of the quadratic equation with real coefficients on complex domain\r\n" );
document.write( "\r\n" );
document.write( "        - Solution of the quadratic equation with complex coefficients on complex domain\r\n" );
document.write( "\r\n" );
document.write( "        - Solved problems on taking roots of complex numbers\r\n" );
document.write( "\r\n" );
document.write( "        - Solved problems on arithmetic operations on complex numbers\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );