Complex Analysis explores the properties and applications of complex numbers and functions, emphasizing their geometric interpretations and analytical techniques.
Visualizing complex numbers and their transformations makes abstract concepts concrete. Use graphing tools or sketch by hand to see how functions act on the complex plane. Focus on how points move, how angles and distances change, and try to relate algebraic operations to geometric movements.
Sketching the mapping of circles under \( f(z) = z^2 \ ).
Using a graphing calculator to visualize the rotation by \( i \ ).