document.write( "Question 1066889: The complex numbers z,z^4 and z^5 where z = cos(2pi/7)+i sin(2pi/7) are represented by the points P,Q and R respectively in the Argand Diagram. If triangle PQR is isosceles, state which sides are equal and it's angles in terms of pi. \n" ); document.write( "

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\n" ); document.write( "The complex numbers z,z^4 and z^5 where z = cos(2pi/7)+i sin(2pi/7) are represented by the points P,Q and R respectively in the Argand Diagram.
\n" ); document.write( "If triangle PQR is isosceles, state which sides are equal and it's angles in terms of pi.
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\n" ); document.write( "\n" ); document.write( "\"Argand diagram\" is a \"scientific name\" for the simple classical complex plane with the complex numbers presented by the corresponding points.\r
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document.write( "So, we have the unit circle with the points \r\n" );
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document.write( "P = z  = cos(2pi/7)+i sin(2pi/7)\r\n" );
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document.write( "Q =  = cos(8pi/7)+i sin(8pi/7)\r\n" );
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document.write( "R =  = cos(10pi/7)+i sin(10pi/7)\r\n" );
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document.write( "in it.\r\n" );
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document.write( "The arc between the points z and  is  (the difference of arguments of these complex numbers).\r\n" );
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document.write( "The arc between the points z and  is again .\r\n" );
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document.write( "So, the triangle PQR has congruent sides PQ and PR, since they tighten congruent arcs.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On complex numbers see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Complex numbers and arithmetic 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
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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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