Can Termwise Differentiation Be Applied to the Series Ʃ(2+3i)^(2+i)n?

[sgonzalez90]

Ʃ(2+3i)^(2+i)n

Since there is no declared z (complex analysis)
in this problem would we take this differentiation with respect to n?

If so, my answer was

Ʃ n(2+3i)^(2+i)n-1

 

[Mute]

Your description of the problem is too ambiguous. What is your summation variable? Is it i or n? Or is i the imaginary number? And is n supposed to be in the power with (2+i)? Is n supposed to be an integer or can it be any number (real or complex)?

 

[sgonzalez90]

The summation index is n so 0 to inf and i is an imaginary number. In all the problems we have seen we are given z because z = x + iy, but here none is given..so I'm unsure if it should just be zero or if we should assume this is z^u or u^z? I'm not sure, the professor didn't specify.

 

[gDavidov]

= \Sigma r^{n}, with r = (2+3i)^(2+i), but |r| = 4.86... > 1 \Rightarrow the sum diverges, so it doesn't even make sense to define it as a function (at least not in the traditional simple way). Therefore you can't take any derivative.