document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164201>Question 164201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble with these two questions. Can someone please explain.\r<BR>\n" );
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document.write( "1. 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(a^2 + b^2). Which of the following is true for all complex numbers? How did you get to that conclusion?<BR>\n" );
document.write( "A) All of the following<BR>\n" );
document.write( "B) z*conj(z) = [modulus(z)]^2 <BR>\n" );
document.write( "C) z + conj(z) = 2a<BR>\n" );
document.write( "D) z - conj(z) = 2bi <BR>\n" );
document.write( "E) None of the above\r<BR>\n" );
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document.write( "2. Using the definition of “size” of z from problem #1, which of the following is largest? How did you get to that conclusion?<BR>\n" );
document.write( "A) 3i<BR>\n" );
document.write( "B) -7<BR>\n" );
document.write( "C) 4<BR>\n" );
document.write( "D) -2i<BR>\n" );
document.write( "E) 4 + 4i<BR>\n" );
document.write( "F) None of the above <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120992 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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/cgi-bin/show-face.mpl?user=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) All of the following<BR>\n" );
document.write( "B) z*conj(z) = [modulus(z)]^2 <BR>\n" );
document.write( "C) z + conj(z) = 2a<BR>\n" );
document.write( "D) z - conj(z) = 2bi <BR>\n" );
document.write( "E) None of the above \r<BR>\n" );
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document.write( "B) right because (a+bi)(a-bi)=a^2-b^2i^2=a^2+b^2=[modulus(z)]^2 <BR>\n" );
document.write( "C) right because (a+bi)+(a-bi)=2a<BR>\n" );
document.write( "D) right because (a+bi)-(a-bi)=2bi\r<BR>\n" );
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document.write( "A) 3i  size is sqrt(9)=3<BR>\n" );
document.write( "B) -7  size is sqrt(49)=7<BR>\n" );
document.write( "C) 4   size is sqrt(16)=4<BR>\n" );
document.write( "D) -2i size is sqrt(4)=2<BR>\n" );
document.write( "E) 4 + 4i size is sqrt(16+16)=sqrt(32)\r<BR>\n" );
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document.write( "so the largest is B) <BR>\n" );
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