document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319283>Question 319283</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Let z = a + bi represent a general complex number. As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a + bi) is the complex number a-bi. Also, the modulus of z, modulus(z) is the \"size\" of z, or SQRT(a2 + b2). Which of the following is true for all complex numbers?\r<BR>\n" );
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document.write( "I am having a really hard time with this problem. Help would be greatly appreciated.<BR>\n" );
document.write( "Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #228607 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=228607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let z = a + bi represent a general complex number. <BR>\n" );
document.write( "As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a + bi) is the complex number a-bi. <BR>\n" );
document.write( "Also, the modulus of z, modulus(z) is the \"size\" of z, or SQRT(a2 + b2). Which of the following is true for all complex numbers? <BR>\n" );
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document.write( "A All of the following<BR>\n" );
document.write( "False because E is not true<BR>\n" );
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document.write( "B z*conj(z) = [modulus(z)]^2<BR>\n" );
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document.write( "true because (a+bi)(a-bi) = a^2+b^2 which is the square of the modulus<BR>\n" );
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document.write( "C z + conj(z) = 2a<BR>\n" );
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document.write( "true because a+bi + a-bi = 2a<BR>\n" );
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document.write( "D z - conj(z) = 2bi<BR>\n" );
document.write( "true because a+bi -(a-bi) = a+bi-a+bi = 2bi<BR>\n" );
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document.write( "E None of the above<BR>\n" );
document.write( "False because b, c, and d are all true<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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