document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108169>Question 1108169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the square roots of z=5&#8722;12i  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723161 by </B><A HREF=/tutors/aboutme.mpl?userid=abdulaleem><B>abdulaleem(11)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=abdulaleem><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=abdulaleem><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that a+bi is a square root of 5 + 12i. <BR>\n" );
document.write( "Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i. <BR>\n" );
document.write( "Equate real and imaginary parts: <BR>\n" );
document.write( "a^2 - b^2 = 5 <BR>\n" );
document.write( "2ab = 12 ==> b = 6/a. \r<BR>\n" );
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document.write( "So, a^2 - (6/a)^2 = 5 <BR>\n" );
document.write( "==> a^2 - 36/a^2 = 5 <BR>\n" );
document.write( "==> a^4 -5a^2 - 36 = 0. <BR>\n" );
document.write( "==> (a^2 -9)(a^2 + 4) = 0. <BR>\n" );
document.write( "Since a must be real, a = 3 or -3. <BR>\n" );
document.write( "This gives b = 2 or -2, respectively. \r<BR>\n" );
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document.write( "Thus, we have two square roots: 3+2i or -3-2i. </SPAN>\n" );
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