document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201677>Question 1201677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE do GIVE CoRRECT AnSwers\r<BR>\n" );
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document.write( "1. Convert the rectangular form of the complex number  2-2i<BR>\n" );
document.write( " into polar form. Show all work and label the modulus and argument.\r<BR>\n" );
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document.write( "2. Find all cube roots of the complex number 64(cos(219 degree) + i sin (219 degree)). Leave answers in polar form and show all work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836152 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=836152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Edit: Sorry I had a brainfart. I mentioned the angle in Q2 when it should have been Q4.<BR>\n" );
document.write( "I have fixed the mistake.\r<BR>\n" );
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document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
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document.write( "2-2i = 2 + (-2)i <BR>\n" );
document.write( "this is written in the form a+bi<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = -2\r<BR>\n" );
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document.write( "r = modulus<BR>\n" );
document.write( "r = sqrt(a^2+b^2)<BR>\n" );
document.write( "r = sqrt((2)^2+(-2)^2)<BR>\n" );
document.write( "r = sqrt(4+4)<BR>\n" );
document.write( "r = sqrt(8)<BR>\n" );
document.write( "r = sqrt(4*2)<BR>\n" );
document.write( "r = sqrt(4)*sqrt(2)<BR>\n" );
document.write( "r = 2*sqrt(2)\r<BR>\n" );
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document.write( "theta = argument<BR>\n" );
document.write( "theta = arctan(b/a)<BR>\n" );
document.write( "theta = arctan(-2/2)<BR>\n" );
document.write( "theta = arctan(-1)<BR>\n" );
document.write( "theta = -45°<BR>\n" );
document.write( "Add 360 degrees to find a coterminal angle in the range 0 ≤ theta < 360<BR>\n" );
document.write( "-45+360 = 315\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "r = 2*sqrt(2)<BR>\n" );
document.write( "theta = 315°\r<BR>\n" );
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document.write( "The polar point (r, theta) is <font color=red>(2*sqrt(2), 315°)</font>\r<BR>\n" );
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document.write( "Another way you could express the answer would be to say the following<BR>\n" );
document.write( "z = r*( cos(theta) + i*sin(theta) )<BR>\n" );
document.write( "z = <font color=red>2*sqrt(2)*( cos(315°) + i*sin(315°) )</font><BR>\n" );
document.write( "z = <font color=red>2*sqrt(2)*cis(315°)</font><BR>\n" );
document.write( "where \"cis\" is shorthand for \"cosine i sine\"<BR>\n" );
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