document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085359>Question 1085359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complex numbers are often used when dealing with alternating current (AC) circuits. In the equation V = IZ, V is voltage, I is current, and Z is a value known as impedance. If V = 1-i and Z=1+3i, find I. Express your answer as a complex number in the form a+bi, where a and b are real numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699412 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1-i=I(1+3i)<BR>\n" );
document.write( "I = (1-i)/(1+3i)<BR>\n" );
document.write( "multiply numerator and denominator by conjugate 1-3i.  The denominator will become 1-9*i^2=1+9=10<BR>\n" );
document.write( "The numerator will be expanded to be 1-3i-i+3i^2=1-4i-3=-2-4i<BR>\n" );
document.write( "This is -2-4i/10<BR>\n" );
document.write( "divide numerator and denominator by -2<BR>\n" );
document.write( "-(1+2i)/5 </SPAN>\n" );
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