document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475313>Question 475313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sir,<BR>\n" );
document.write( "my question is how to dissolve imaginary part in an equation completely.<BR>\n" );
document.write( "the equation is of the form cos(theeta)+jsin(theeta) & j,the imaginary  part should be completely taken out by simplifying  & iam not finding the solution.Pls help me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325936 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=325936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok so the equation is a complex number in polar form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+r%2A%28cos%28theta%29+%2B+j%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"z+=+r%2A%28cos%28theta%29+%2B+j%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where r is the modulus or the magnitude of the distance from origin on complex plane.<BR>\n" );
document.write( "To eliminate the imaginary part, multiply by the conjugate.<BR>\n" );
document.write( "The conjugate is just the same number with the imaginary part having the opposite sign.<BR>\n" );
document.write( "Ex: z = 2 + 3j, conjugate = 2 - 3j<BR>\n" );
document.write( "In polar form the conjugate would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2A%28cos%28theta%29+-+j%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"r%2A%28cos%28theta%29+-+j%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So multiply by the conjugate:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28cos%28theta%29+%2B+j%2Asin%28theta%29%29+%2A+r%28cos%28theta%29+-+j%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"r%28cos%28theta%29+%2B+j%2Asin%28theta%29%29+%2A+r%28cos%28theta%29+-+j%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28cos%5E2%28theta%29+%2B+j%2Asin%28theta%29%2Acos%28theta%29-j%2Asin%28theta%29%2Acos%28theta%29-j%5E2%2Asin%5E2%28theta%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Middle term cancels<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28cos%5E2%28theta%29-j%5E2%2Asin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"r%5E2%28cos%5E2%28theta%29-j%5E2%2Asin%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "j^2 = -1<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28cos%5E2%28theta%29%2B+sin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"r%5E2%28cos%5E2%28theta%29%2B+sin%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "trig identity, sin^2 + cos^2 = 1<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope that answered your question. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );