I've posted before about my fractal project, and this is something else that is related. The function:
where
.
The derivative along this line:
for a new real variable
.
I'm trying to find when the real and/or imaginary parts equal zero.
Is there any other way to solve these equations without splitting
into
and
just because it is so messy and long? I know one method of removing the imaginary terms from the bottom by multiplying top and bottom by
, factoring
out of the denominator, and multiplying numerator and denominator by
resulting in a denominator of
. It's still messy with a numerator of
but now, algebraically, the worst part is
. I'd appreciate any suggestions.