document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085385>Question 1085385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What complex number equals (1 + isqrt{3})^6? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699459 by </B><A HREF=/tutors/aboutme.mpl?userid=natolino_2017><B>natolino_2017(77)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=natolino_2017><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we have two ways (at least) to answer this:\r<BR>\n" );
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document.write( "i) using Newton binomial:\r<BR>\n" );
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document.write( "(1+isqrt(3))^6 = (6C0)(isqrt(3))^0 + (6C1)(isqrt(3))^1 +(6C2)(isqrt(3))^2 + (6C3)(isqrt(3))^3 +(6C4)(isqrt(3))^4 + (6C5)(isqrt(3))^5 + (6C6)(isqrt(3))^6\r<BR>\n" );
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document.write( "= 1 + 6sqrt(3)*i - 45 - 60sqrt(3)i + 135 + 54sqrt(3)i - 27 = 64\r<BR>\n" );
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document.write( "ii) Using the Moivre's formula:\r<BR>\n" );
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document.write( "(1+isqrt(3)) = 2cis(60°)\r<BR>\n" );
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document.write( "so (1+isqrt(3))^6 = 2^6(cis(6*60°) = 64cis(360) =64cis(0) =64(cos(0) +i sin(0)) = 64.\r<BR>\n" );
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document.write( "@natolino_ </SPAN>\n" );
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