On an Alternative View to Complex Calculus

A review of complex calculus in use today, shows that new techniques to solve multivalued nature of logarithmic functions that cause lots of difficulties to work on this subject. One such techniques is re-orientation of complex space to the wider space B which will be explained completely in the following thesis. The aim of this study is to provide alternative complex calculus on multiplicative and bi-geometric cases. First of all, multiplicative complex calculus was accomplished, then, we found that there are still some drawbacks on this method, so bi-geometric case of complex calculus was established and the results showed that the mentioned drawbacks that are demonstrated in this study, do not appear in bi-geometric case. Further research is recommended to asses the Fourier series, Taylor polynomial and Laurent seried in bi-geometric complex calculus. Keywords: Newtonian Calculus, Bi-geometric complex calculus, Logarithm, Multiplicative complex calculus.