E1: Initialize! The red point of the array will be at (+1, 0), the point to be used as a divisor for the array at (1, i). Follow the construction of the quotient in the u plane for all points of the array.
E2: Change the length of the divisor vector without changing its direction. How and to what degree does that shift the array in the u plane?
E3: Rotate the divisor vector. What is the result the in the u plane? Try to formulate it quantitatively.
E4: Change both vectors. What determines the length (r) and the direction (angle) of the quotient vector? Why and how does the orientation and the size of the array change?
E5: Repeat the experiment for a single point by reducing the array to a point.
E 5: The division process is most easily understood when both complex numbers z1 and z2 are described by the length r und direction φ of their vectors:
z1 = r1 ∙ e iφ_1
z2 = r2 ∙ e iφ_2
➾ u = z1 / z2 = r1 / r2 ∙ e iφ_1 / e iφ_2 = r1 / r2∙ e i(φ_1 - φ_2)
Describe this algorithm in words!