document.write( "Question 1100156: evaluate |1+2i/2+3i| \n" ); document.write( "
Algebra.Com's Answer #714652 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  \"%281%2B2i%29%2F%282%2B3i%29\" = \r\n" );
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document.write( "= \"%28%281%2B2i%29%2F%282%2B3i%29%29%28%282-3i%29%2F%282-3i%29%29\" =\r\n" );
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document.write( "= \"%28%281%2B2i%29%282-3i%29%29%2F%284%2B9%29\" =\r\n" );
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document.write( "= \"%282-3i%2B4i%2B6%29%2F13\" =\r\n" );
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document.write( "= \"%288%2Bi%29%2F13\" = \"8%2F13+%2B+i%2A%281%2F13%29\".\r\n" );
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document.write( "The modulus of this complex number is \r\n" );
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document.write( "\"sqrt%28%288%2F13%29%5E2+%2B+%281%2F13%29%5E2%29\" = \"sqrt%2864%2F169+%2B+1%2F169%29%29\" = \"sqrt%2865%2F169%29\" = \"sqrt%2865%29%2F13\".\r\n" );
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document.write( "Answer.  |(1+2i)/(2+3i)| = \"sqrt%2865%29%2F13\".\r\n" );
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\n" ); document.write( "On complex numbers see the lessons in this site \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
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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
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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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\n" ); document.write( "Be aware: there is an ERROR in calculations by @josgarithmetic.\r
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