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.