standard_description: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
problem_activity: Task
Let $z = 1 + i$ where $i^2 = -1$.   Calculate $z^2, z^3,$ and  $z^4$.
Graph $z, z^2, z^3,$ and  $z^4$ in the complex plane.  What do you notice about the positions of these  numbers?
What is $z^{100}$?  Explain.


aligns: no