document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53194>Question 53194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The set of non-zero complex numbers is closed under which operation(s)?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35691 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The set of non-zero complex numbers is closed under which operation(s)? <BR>\n" );
document.write( "ADDITION<BR>\n" );
document.write( "(A+IB)+(P+IQ)=(A+P)+I(B+Q)...IF A=-P AND B=-Q,IT GIVES ZERO WHICH IS NOT IN THE SET.HENCE NOT CLOSED<BR>\n" );
document.write( "SIMILARLY<BR>\n" );
document.write( "MULTIPLICATION<BR>\n" );
document.write( "(A+IB)(P+IQ)=(AP-BQ)+I(AQ+BP)...HERE IF AP=BQ THEN AQ CANNOT EQUAL -BP AND <BR>\n" );
document.write( "VISEVERSA..HENCE IT IS NONZERO COMPLEX NUMBER..SO IT IS CLOSED<BR>\n" );
document.write( "DIVISION<BR>\n" );
document.write( "(A+IB)/(P+IQ)=(A+IB)(P-IQ)/(P^+Q^2)=[(AP+BQ)+I(BP-AQ)]/(P^2+Q^2)<BR>\n" );
document.write( "FOR SAME REASON AS ABOVE ..WE GET THIS ALSO AS CLOSED </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );