Questions: Find the graph of this function as the value of n increases, starting from n=1. f(n)=(5/16+11/12 i)^n

Solution Steps

The function f(n) = (5/16 + (11/12)i)^n represents a complex number raised to the power of n. As n increases, the complex number is repeatedly multiplied by itself.

When n=1, the function simply evaluates to the complex number itself. For n=2, the complex number is squared, for n=3 it is cubed, and so on. Graphically, multiplying complex numbers causes a rotation and scaling in the complex plane.

The first graph shows the values of f(n) for n = 1 to 6. The second graph represents values for n between 7 and approximately 12. The third graph demonstrates the plotted points for n roughly between 13 and 18.

Final Answer