document.write( "Question 1180531: Find the 3 cube roots of i in polar form. \n" ); document.write( "
Algebra.Com's Answer #810237 by ikleyn(52810)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Find the 3 cube roots of i in polar form.
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "    i = (1, \"pi%2F2\") = (1,90°)  in polar form  (the modulus is 1;  the argument is  \"pi%2F2\",  or  90°).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use deMoivre formula.  The three cubic roots of \" i \" are\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "a)  (1, \"pi%2F6\") = (1,30°);\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "b)  (1, \"pi%2F6+%2B+%282pi%2F3%29\") = (1, \"pi%2F6+%2B+4pi%2F6\") = (1, \"5pi%2F6\") = (1,150°);\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "c)  (1, \"pi%2F6+%2B+%284pi%2F3%29\") = (1, \"pi%2F6+%2B+8pi%2F6\") = (1, \"9pi%2F6\") = (1,270°).\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );