document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=300834>Question 300834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am looking for a general solution to a complex number raised to a complex power. I recall that Euler had a solution, but I can't recall what it was. However, it was in the form of (something here) + i (something here), and used logarithms heavily (as is an Euler trademark). Any help will be greatly appreciated. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #215795 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=215795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "To calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a\ +\ bi)^{c\ +\ di}\">:\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \varphi\ =\ \arg(a\ +\ bi)\ =\ \pm\arctan\frac{b}{a}\"> taking the sign appropriately so that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ +\ bi\ =\ r(\cos\varphi+i\sin\varphi)\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \theta\ =\  c\ \cdot\ \varphi\ +\ \frac{1}{2}d\ \cdot\ \ln\left(a^2\,+\,b^2\right)\">\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a\ +\ bi)^{c\ +\ di} =\ \left(a^2\,+\,b^2\right)^{c/2}\,\cdot\,e^{-d\varphi}\,\cdot\,\left(\cos\theta\ +\ i\sin\theta\right)\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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