document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981148>Question 981148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express the complex number in trigonometric form. \r<BR>\n" );
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document.write( "2 - 2i\r<BR>\n" );
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document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602201 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=602201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-2i ALIGN=MIDDLE  ALT=\"2-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bbi ALIGN=MIDDLE  ALT=\"a%2Bbi\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2 ALIGN=MIDDLE  ALT=\"a+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-2 ALIGN=MIDDLE  ALT=\"b+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Trig form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2A%28cos%28theta%29+%2B+i%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"r%2A%28cos%28theta%29+%2B+i%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We will use the following formulas:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%28a%5E2+%2B+b%5E2%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28a%5E2+%2B+b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+arctan%28b%2Fa%29 ALIGN=MIDDLE  ALT=\"theta+=+arctan%28b%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "Compute the value of r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%28a%5E2+%2B+b%5E2%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28a%5E2+%2B+b%5E2%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+=+sqrt%282%5E2+%2B+%28-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%282%5E2+%2B+%28-2%29%5E2%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+=+sqrt%284%2B4%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%284%2B4%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+=+sqrt%288%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%288%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+=+sqrt%284%2A2%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%284%2A2%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+=+sqrt%284%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%284%29%2Asqrt%282%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+=+2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"r+=+2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "Now find theta (use a calculator or unit circle).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+arctan%28b%2Fa%29 ALIGN=MIDDLE  ALT=\"theta+=+arctan%28b%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+arctan%28-2%2F2%29 ALIGN=MIDDLE  ALT=\"theta+=+arctan%28-2%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+arctan%28-1%29 ALIGN=MIDDLE  ALT=\"theta+=+arctan%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+-pi%2F4 ALIGN=MIDDLE  ALT=\"theta+=+-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+-pi%2F4%2B2pi ALIGN=MIDDLE  ALT=\"theta+=+-pi%2F4%2B2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > Adding on 2pi to get the angle between 0 and 2pi<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+7pi%2F4 ALIGN=MIDDLE  ALT=\"theta+=+7pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "So the trig form is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2A%28cos%28theta%29+%2B+i%2Asin%28theta%29%29=2%2Asqrt%282%29%2A%28cos%287pi%2F4%29+%2B+i%2Asin%287pi%2F4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "Final Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29%2A%28cos%287pi%2F4%29+%2B+i%2Asin%287pi%2F4%29%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29%2A%28cos%287pi%2F4%29+%2B+i%2Asin%287pi%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: this is the radian form </SPAN>\n" );
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