document.write( "Question 565116: Use Demoivre's Theorem to find the indicated power of the complex number
\n" ); document.write( "(2+2squareroot3i)^6
\n" ); document.write( "not even sure how to start this
\n" ); document.write( "help would be greatly appreciated \n" ); document.write( "

Algebra.Com's Answer #365677 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "You have to know 2 things:\r\n" );
document.write( "\r\n" );
document.write( "1. How to change from a+bi form to trig form r(cosq + i sinq)\r\n" );
document.write( "\r\n" );
document.write( "use tanq =  and r = \r\n" );
document.write( "\r\n" );
document.write( "2.  How to raise a complex number in trig form using DeMoivre's\r\n" );
document.write( "   formula:\r\n" );
document.write( "\r\n" );
document.write( "[r(cosq + i sinq)]ⁿ = rⁿ[cos(nq) + i·sin(nq)]\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2+2squareroot3i)^6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1. To change from 2+2i form to trig form r(cosq + i·sinq)\r\n" );
document.write( "\r\n" );
document.write( "use tanq =  = \r\n" );
document.write( "therefore q = 60°\r\n" );
document.write( "\r\n" );
document.write( "and r =  =  =  =  = 4\r\n" );
document.write( "\r\n" );
document.write( "So 2 + 2i = 4(cos60° + i·sin60°) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2. To raise this complex number in trig form using DeMoivre's\r\n" );
document.write( "   formula:\r\n" );
document.write( "\r\n" );
document.write( "[4(cos60° + i·sin60°)]⁶ = 4⁶[cos(6·60°) + i·sin(6·60)] =\r\n" );
document.write( "4096(cos360° + i·sin360°) = 4096(cos0° + i·sin0°) = \r\n" );
document.write( "4096(1+i·0) = 4096(1+0) = 4096(1) = 4096.\r\n" );
document.write( "\r\n" );
document.write( "answer: 4096.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );