Series that Begin with (a+b*i)^n - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-24T10:15:28Z http://mathoverflow.net/feeds/question/61774 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61774/series-that-begin-with-abin Series that Begin with (a+b*i)^n Marvin Ray Burns 2011-04-15T01:51:44Z 2011-04-15T01:51:44Z <p>Since -1 = i^2 I thought that there could be some meaning behind alternating series that instead of begining with (-1)^n begin with (a+b*i)^n for a and b != 0; does anyone know where I can find out more about such a series? As an example,<BR>$\sum _{n=0}^{\infty } \frac{(a+i b)^n}{n!}=e^{a+i b}$ </p>