document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57257>Question 57257</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618073639/algebrahomeworkh>Applied College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Verify that P(x) = x^3 - x^2 - ix^2 - 20x + ix + 20i has a zero of i and that its conjugate -i is not a zero. Explain why this does not contradict the Conjugate Pair Theorem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38964 by </B><A HREF=/tutors/aboutme.mpl?userid=Scriptor><B>Scriptor(36)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Scriptor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=38964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Just fill in i in your function and check if it becomes 0. <BR>\n" );
document.write( "Make use of the property that i² = -1\r<BR>\n" );
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document.write( "P(i) = i³ - i² -i*(i²) -20i + i*i + 20i\r<BR>\n" );
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document.write( "     = -i + 1 + i - 20i - 1 + 20i\r<BR>\n" );
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document.write( "     = 0\r<BR>\n" );
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document.write( "Check for yourself that P(-i) is NOT equal to zero (same mehod as above)\r<BR>\n" );
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document.write( "This does not contradict the Conjugate Pair Theorem, because not all the coefficients of P(x) are real.\r<BR>\n" );
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document.write( "Greets,<BR>\n" );
document.write( "Scriptor </SPAN>\n" );
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