document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85106>Question 85106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express the complex number -2 sqrt2 + 2 sqrt2i in the trigonometric form r(cos theta +i sin theta) or rcis(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61323 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=61323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> express the complex number -2 sqrt2 + 2 sqrt2i in the trigonometric form r(cos theta +i sin theta) or rcis(theta)<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "If complex number is a+bi, then trig form is<BR>\n" );
document.write( "rcis(theta) where r=sqrt(a^2+b^2) and theta=arc tan(b/a) is the appropriate<BR>\n" );
document.write( "quadrant.<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Your problem:<BR>\n" );
document.write( "r= sqrt[-2sqrt2)^2 + (2sqrt2)^2] = sqrt[8+8] = 4<BR>\n" );
document.write( "theta = arctan[(2sqrt2)/-2sqrt2]=arctan(-1)= 135 degrees or 315 degrees<BR>\n" );
document.write( "But b is positive and a is negative so theta is in the 2nd quadrant.<BR>\n" );
document.write( "Therefore theta = 135 degrees or (3/4)pi.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "trig form is 4cis135 or 4cis((3/4)pi)<BR>\n" );
document.write( "===========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );