document.write( "Question 1172294: Convert -√3- i to polar form \r
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Algebra.Com's Answer #797276 by ikleyn(52847)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The polar form is  \"-sqrt%283%29+-+i\" = r * ( cos(a) + i*sin(a) ),\r\n" );
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document.write( "where \"r\" is the polar radius and \"a\" is the polar angle.\r\n" );
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document.write( "So, our goal is to find the polar radius r and the polar angle \"a\".\r\n" );
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document.write( "    r = \"sqrt%28x%5E2+%2B+y%5E2%29\" = \"sqrt%28%28-sqrt%28%283%29%29%5E2+%2B+%28-i%29%5E2%29%29\" = \"sqrt%283%2B1%29\" = \"sqrt%284%29+\" = 2.\r\n" );
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document.write( "    tan(a) = \"y%2Fx\" = \"%28-1%29%2F%28-sqrt%283%29%29\" = \"1%2Fsqrt%283%29\" = \"sqrt%283%29%2F3\".\r\n" );
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document.write( "Therefore,  a = \"7pi%2F6\"    ( taking into account that the angle \"a\" is in QIII ).\r\n" );
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document.write( "Thus the polar form is, finally,  \"-sqrt%283%29+-+i\" = \"2%2A%28cos%287pi%2F6%29+%2B+i%2Asin%287pi%2F6%29%29\" = (2, \"7pi%2F6\") = \"2%2Acis%287pi%2F6%29\".    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is a bunch of my lessons on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Complex numbers and arithmetical operations on them\r
\n" ); document.write( "\n" ); document.write( "    - Complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Addition and subtraction of complex numbers in complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Multiplication and division of complex numbers in complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Raising a complex number to an integer power\r
\n" ); document.write( "\n" ); document.write( "    - How to take a root of a complex number\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the quadratic equation with real coefficients on complex domain\r
\n" ); document.write( "\n" ); document.write( "    - How to take a square root of a complex number\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the quadratic equation with complex coefficients on complex domain\r
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\n" ); document.write( "\n" ); document.write( "    - Solved problems on taking roots of complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic operations on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problem on taking square root of complex number\r
\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problem on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on de'Moivre formula\r
\n" ); document.write( "\n" ); document.write( "    - Calculating the sum 1*sin(1°) + 2*sin(2°) + 3*sin(3°) + . . . + 180*sin(180°) \r
\n" ); document.write( "\n" ); document.write( "    - A curious example of an equation in complex numbers which HAS NO a solution\r
\n" ); document.write( "\n" ); document.write( "    - Solving one non-standard equation in complex numbers\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Complex numbers\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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