Question 1199306
<pre>
Ikleyn claims that one must never write "ln(x)" but only "ln(|x|)".  But most any
teacher would write "ln(x)" and "log<sub>b</sub>(x)".  I suppose Ikleyn would also
say that in real numbers one must never write √(x) but only √(|x|).  However,
domains are well-known for these functions in real numbers.  It is not necessary
to complicate the notation.

To prove deMoivre's theorem students are often taught Euler's equation:

{{{e^(xi)=cos(x)+i*sin(x)}}} which implies {{{e^(pi*i)=-1}}} or {{{ln(-1)=pi*i}}}

In complex analysis, an undergraduate mathematics course, logarithms of negative
numbers are well defined as complex numbers.  

Edwin</pre>