document.write( "Question 1207479: If z1 , z2 are two complex numbers , |z1|=|z2| , and Arg(z1 + z2) = pi/4 ,find Arg(z1×z2) \n" ); document.write( "

Algebra.Com's Answer #845373 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "arg(z1*z2) is always equal to arg(z1) + arg(z2)    (by the modulo of ).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the other side, if  |z1| = |z2|,  then arg(z1+z2) =  \r\n" );
document.write( "\r\n" );
document.write( "according to the parallelogram rule of adding vectors (= complex numbers), which\r\n" );
document.write( "\r\n" );
document.write( "is in this case the \"rhombus\" rule of adding vectors.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this, we conclude that, under given conditions,\r\n" );
document.write( "\r\n" );
document.write( "    arg(z1*z2) = arg(z1) + arg(z2) =  = 2*arg(z1+z2) =  = .    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );