document.write( "Question 1122243: Please help me convert a complex number to polar form and exponential form.
\n" ); document.write( "2+2(sqrt3i) \n" ); document.write( "
Algebra.Com's Answer #738309 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "a + bi = \"2+%2B+2%2Asqrt%283%29%2Ai\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "a = 2;  b = \"2%2Asqrt%283%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The mudulus  r = \"sqrt%28a%5E2+%2B+b%5E2%29\" = \"sqrt%282%5E2+%2B+%282%2Asqrt%283%29%29%5E2%29\" = \"sqrt%284+%2B+4%2A3%29\" = \"sqrt%2816%29\" = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The argument  \"theta\" = \"arctan%28b%2Fa%29\" = \"arctan%28%282%2Asqrt%283%29%29%2F2%29\" = \"arctan%28sqrt%283%29%29\" = \"pi%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Polar form:  a + bi = \"2+%2B+2%2Asqrt%283%29%2Ai\" = (4,\"pi%2F3\"),   where first argument \"4\" is the modulus and the second argument  \"pi%2F3\"  is the polar angle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the same as  the Trigonometric form of a complex number a + bi = \"2+%2B+2%2Asqrt%283%29%2Ai\" = \"4%2A%28cos%28pi%2F3%29+%2B+i%2Asin%28pi%2F3%29%29\" = \"4%2A%28%281%2F2%29+%2B+i%2A%28sqrt%283%29%2F2%29%29\" = \"4%2Acis%28pi%2F3%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Exponential form:  a + bi = \"2+%2B+2%2Asqrt%283%29%2Ai\" = 4*e^(i*(pi/3)) = \"4%2Ae%5E%28i%2A%28pi%2F3%29%29\".\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On complex numbers, see the lessons\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
\n" ); document.write( "
\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( "    - A curious example of an equation in complex numbers which HAS NO a solution\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Complex numbers\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );