document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090711>Question 1090711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express the complex number in trigonometric form. \r<BR>\n" );
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document.write( "6 - 6i\r<BR>\n" );
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document.write( "Please write the answer in radians,  andshow work<BR>\n" );
document.write( "THANK YOU </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705173 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "This is the trigonometric form of a complex number where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29 ALIGN=MIDDLE  ALT=\"abs%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the modulus and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the angle created on the complex plane.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=a%2Bbi=abs%28z%29%28cos%28theta%29%2Bi%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"z=a%2Bbi=abs%28z%29%28cos%28theta%29%2Bi%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The modulus of a complex number is the distance from the origin on the complex plane.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28z%29=sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=a%2Bbi ALIGN=MIDDLE  ALT=\"z=a%2Bbi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute the actual values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29=sqrt%286%5E2%2B%28-6%29%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28z%29=sqrt%286%5E2%2B%28-6%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29=sqrt%2836%2B36%29 ALIGN=MIDDLE  ALT=\"abs%28z%29=sqrt%2836%2B36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29=sqrt%282%2A36%29 ALIGN=MIDDLE  ALT=\"abs%28z%29=sqrt%282%2A36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29=6sqrt%282%29 ALIGN=MIDDLE  ALT=\"abs%28z%29=6sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=tan%5E-1%28-6%2F6%29 ALIGN=MIDDLE  ALT=\"theta=tan%5E-1%28-6%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since inverse tangent of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2F6 ALIGN=MIDDLE  ALT=\"-6%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces an angle in the fourth quadrant, the value of the angle is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-pi%2F4 ALIGN=MIDDLE  ALT=\"+-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "Substitute the values of <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;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29=6sqrt%282%29 ALIGN=MIDDLE  ALT=\"abs%28z%29=6sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bbi=abs%28z%29%28cos%28theta%29%2Bi%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"a%2Bbi=abs%28z%29%28cos%28theta%29%2Bi%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-6i=6sqrt%282%29%28cos%28+-pi%2F4%29%2Bi%2Asin%28+-pi%2F4%29%29 ALIGN=MIDDLE  ALT=\"6-6i=6sqrt%282%29%28cos%28+-pi%2F4%29%2Bi%2Asin%28+-pi%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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