document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=396290>Question 396290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am stuggling very much on these two questions on complex numbers. If you can help, it would be very much appreciated. Thank you!\r<BR>\n" );
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document.write( "Directions: In these questions exact values for &#952; are to be used and answers are to be expressed as a radical.\r<BR>\n" );
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document.write( "1. If z=10(cos225°+i*sin225°) in trigonometric form find z in standard form.\r<BR>\n" );
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document.write( "2. If z=6sqrt(3)(cos330°+i*sin330°) in trigonometric form find z in standard form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281147 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=281147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm guessing that what you're really having<BR>\n" );
document.write( "problems with is trig. Do you have a solid foundation<BR>\n" );
document.write( "in trig? Can you easily convert cos 225 degrees to<BR>\n" );
document.write( "an expression with radicals?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225+=+180+%2B+45 ALIGN=MIDDLE  ALT=\"225+=+180+%2B+45\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees, so you have a vector in<BR>\n" );
document.write( "the 3rd quadrant where the cosine and sine are both negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28225%29+=+-+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"cos%28225%29+=+-+1%2Fsqrt%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=sin%28225%29+=+-+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sin%28225%29+=+-+1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+10%2A%28-1%2Fsqrt%282%29+-+i%2A%281%2Fsqrt%282%29%29%29 ALIGN=MIDDLE  ALT=\"z+=+10%2A%28-1%2Fsqrt%282%29+-+i%2A%281%2Fsqrt%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%2810%2Fsqrt%282%29%29%2A%28-1+-+i%29 ALIGN=MIDDLE  ALT=\"z+=+%2810%2Fsqrt%282%29%29%2A%28-1+-+i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply top and bottom by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%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=z+=+5%2Asqrt%282%29%2A%28-1+-+i%29 ALIGN=MIDDLE  ALT=\"z+=+5%2Asqrt%282%29%2A%28-1+-+i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note also that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28330%29+=+cos%28360+-+30%29 ALIGN=MIDDLE  ALT=\"cos%28330%29+=+cos%28360+-+30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the angle is in the 4th quadrant and makes<BR>\n" );
document.write( "an angle of 30 with the positive real axis.<BR>\n" );
document.write( "The cosine is positive and the sine is negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28330%29+=+sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28330%29+=+sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28330%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"sin%28330%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can finish as I did in (1)<BR>\n" );
document.write( "  </SPAN>\n" );
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