document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395841>Question 395841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have a big test on complex numbers tomorrow and I am having a very hard time with this particular question:\r<BR>\n" );
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document.write( "Directions: On a complex plane, a point z has been graphed. your\r<BR>\n" );
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document.write( "If cos&#952;=(-8)/(22) and (&#960;)/(2)&#8804;&#952;&#8804;&#960;:\r<BR>\n" );
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document.write( "a) Find z in standard form.<BR>\n" );
document.write( "b) Find z in trigonometric form. (Use whole degrees)\r<BR>\n" );
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document.write( "&#952;= Theta <BR>\n" );
document.write( "&#960;= pi  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280964 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The angle is in the second quadrant, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28theta%29 ALIGN=MIDDLE  ALT=\"sin+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive. By the Pythagorean identity,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2+%28theta%29+%2B+cos%5E2+%28theta%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2+%28theta%29+%2B+cos%5E2+%28theta%29+=+1\"   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=sin%5E2+%28theta%29+%2B+16%2F121+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2+%28theta%29+%2B+16%2F121+=+1\"   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=sin%5E2+%28theta%29+=+105%2F121 ALIGN=MIDDLE  ALT=\"sin%5E2+%28theta%29+=+105%2F121\"   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=sin+%28theta%29+=+sqrt%28105%29%2F11 ALIGN=MIDDLE  ALT=\"sin+%28theta%29+=+sqrt%28105%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the cosine corresponds to the x-coordinate or the real part of z, we say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Re%28z%29+=+4%2F11 ALIGN=MIDDLE  ALT=\"Re%28z%29+=+4%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Likewise, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Im%28z%29+=+%28sqrt%28105%29%2F11%29i ALIGN=MIDDLE  ALT=\"Im%28z%29+=+%28sqrt%28105%29%2F11%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the complex number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+4%2F11+%2B+%28sqrt%28105%29%2F11%29i ALIGN=MIDDLE  ALT=\"z+=+4%2F11+%2B+%28sqrt%28105%29%2F11%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note that we can multiply z by any real constant and the cosine, sine values will still be the same. </SPAN>\n" );
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