Compute and Plot the element of a complex sequence

I'm new tho mathematica.

I have a complex sequence ${z_n}$ with

$z_0:=c$

$z_{n+1}=(z_n)^2+c$ for all $n\in N$

where c is some complex number, I need to plot the first 20 terms of this sequence where $c=-0.5+0.2i$, print the plot and for the value of $c$ in $(a)$ determin it's limit.

The main problem is that i don't know from where to start...

For basic function construction see: http://reference.wolfram.com/language/tutorial/MakingDefinitionsForFunctions.html

You did not explain how you want to plot a complex valued function but here's a start:

c = -0.5 + 0.2 I;
z[0] := c
z[n_Integer?Positive] := z[n - 1]^2 + c

Array[z, 20]

{-0.29 + 0. I, -0.4159 + 0.2 I, -0.367027 + 0.03364 I, -0.366423 +
0.175306 I, -0.396467 + 0.0715275 I, -0.34793 + 0.143283 I, -0.399475 +
0.100295 I, -0.350479 + 0.11987 I, -0.391533 + 0.115976 I, -0.360152 +
0.109183 I, -0.382211 + 0.121355 I, -0.368642 + 0.107233 I, -0.375602 +
0.120939 I, -0.373549 + 0.10915 I, -0.372375 + 0.118454 I, -0.375368 +
0.111781 I, -0.371594 + 0.116082 I, -0.375393 + 0.11373 I, -0.372015 +
0.114613 I, -0.374741 + 0.114724 I}


For plotting complex values perhaps start here: Plotting complex Sine

• The now built-in functions for plotting Julia and Mandelbrot sets might also be of interest to the OP. – J. M. will be back soon May 12 '15 at 23:37