document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124676>Question 1124676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -34/5-3i in polar form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741022 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=741022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The polar form of a complex number is another way to represent a complex number. The form <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;\" > is called the rectangular coordinate form of a complex number. <BR>\n" );
document.write( "The horizontal axis is the real axis and the vertical axis is the imaginary axis. We find the real and complex components in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the vector 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 made with the real axis.\r<BR>\n" );
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document.write( "From Pythagorean Theorem :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By using the basic trigonometric ratios : \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29=a%2Fr ALIGN=MIDDLE  ALT=\"cos%28theta%29=a%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=b%2Fr ALIGN=MIDDLE  ALT=\"sin%28theta%29=b%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiplying each side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   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=a=r%2Acos%28theta%29 ALIGN=MIDDLE  ALT=\"a=r%2Acos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=r%2Asin%28theta%29 ALIGN=MIDDLE  ALT=\"b=r%2Asin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The rectangular form of a complex number is given by:\r<BR>\n" );
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document.write( "<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 values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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=z=r%2Acos%28theta%29%2B%28r%2Asin%28theta%29%29i%26%238201%3B%26%238201%3B%26%238201%3B ALIGN=MIDDLE  ALT=\"z=r%2Acos%28theta%29%2B%28r%2Asin%28theta%29%29i%26%238201%3B%26%238201%3B%26%238201%3B\"   DISABLED_style= \"max-width:90%; height:auto;\" >&#8201;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=r%28cos%28theta%29%2Bi%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"z=r%28cos%28theta%29%2Bi%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z=-34%2F5-3i ALIGN=MIDDLE  ALT=\"+z=-34%2F5-3i\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z=+-6.8+-3i ALIGN=MIDDLE  ALT=\"+z=+-6.8+-3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-6.8 ALIGN=MIDDLE  ALT=\"a=-6.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to write it in polar form, first find the absolute value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   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=r=abs%28z%29=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"r=abs%28z%29=sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-6.8 ALIGN=MIDDLE  ALT=\"a=-6.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%28%28-6.8%29%5E2%2B%28-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"r=sqrt%28%28-6.8%29%5E2%2B%28-3%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=r=sqrt%2846.24%2B9%29 ALIGN=MIDDLE  ALT=\"r=sqrt%2846.24%2B9%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=r=sqrt%2855.24%29 ALIGN=MIDDLE  ALT=\"r=sqrt%2855.24%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=r+ ALIGN=MIDDLE  ALT=\"r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > » <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.43236 ALIGN=MIDDLE  ALT=\"7.43236\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=7.43236%28cos%28theta%29%2Bi%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"z=7.43236%28cos%28theta%29%2Bi%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now find the argument <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " To find argument <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will use one of the following formulas:\r<BR>\n" );
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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;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   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%2B180 ALIGN=MIDDLE  ALT=\"theta=arctan%28b%2Fa%29%2B180\"   DISABLED_style= \"max-width:90%; height:auto;\" >° if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C0 ALIGN=MIDDLE  ALT=\"a%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so you can use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=arctan%28b%2Fa%29%2B180 ALIGN=MIDDLE  ALT=\"theta=arctan%28b%2Fa%29%2B180\"   DISABLED_style= \"max-width:90%; height:auto;\" >° since you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C0 ALIGN=MIDDLE  ALT=\"a%3C0\"   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=theta=arctan%28-3%2F-6.8%29%2B180 ALIGN=MIDDLE  ALT=\"theta=arctan%28-3%2F-6.8%29%2B180\"   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=theta=arctan%283%2F6.8%29%2B180 ALIGN=MIDDLE  ALT=\"theta=arctan%283%2F6.8%29%2B180\"   DISABLED_style= \"max-width:90%; height:auto;\" >° <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=24%B0%2B180 ALIGN=MIDDLE  ALT=\"theta=24%B0%2B180\"   DISABLED_style= \"max-width:90%; height:auto;\" >° <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=204 ALIGN=MIDDLE  ALT=\"theta=204\"   DISABLED_style= \"max-width:90%; height:auto;\" >° \r<BR>\n" );
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document.write( "polar form is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=7.43236%28cos%28204%29%2Bi%2Asin%28204%29%29 ALIGN=MIDDLE  ALT=\"z=7.43236%28cos%28204%29%2Bi%2Asin%28204%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );