document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083651>Question 1083651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283-4i%29 ALIGN=MIDDLE  ALT=\"sqrt%283-4i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in standard form<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697675 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> standard form of a complex number is a + bi, where a and b are real numbers and i is the square root(-1) <BR>\n" );
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document.write( "sqrt(3 - 4i) = a+bi<BR>\n" );
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document.write( "square both sides of =<BR>\n" );
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document.write( "3 - 4i = (a+bi)^2<BR>\n" );
document.write( "3 - 4i = (a^2 + 2abi -b^2)<BR>\n" );
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document.write( "we have two equations in two unknowns<BR>\n" );
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document.write( "1)  3 = a^2 - b^2<BR>\n" );
document.write( "2)  -4i = 2abi<BR>\n" );
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document.write( "solve equation 2 for a<BR>\n" );
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document.write( "a = -4i / 2bi = -2/b<BR>\n" );
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document.write( "substitute for a in equation 1 and solve for b<BR>\n" );
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document.write( "b^4 +3b^2 -4 = 0<BR>\n" );
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document.write( "let u = b^2, then<BR>\n" );
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document.write( "u^2 +3u -4 = 0<BR>\n" );
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document.write( "factor polynomial<BR>\n" );
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document.write( "(u+4) * (u-1) = 0<BR>\n" );
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document.write( "u = -4 and u = 1<BR>\n" );
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document.write( "b^2 = -4 and b^2 = 1<BR>\n" );
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document.write( "b = 2i, -2i, 1, -1, b is real so reject 2i and -2i<BR>\n" );
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document.write( "a = -2/b<BR>\n" );
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document.write( "a = -2 or 2<BR>\n" );
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document.write( "standard form is 2 - i or -2 + i<BR>\n" );
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document.write( ":\r<BR>\n" );
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