Copy of Exploring addition of Complex Numbers

How should A and B be situated so that C is on the Real axis?

How should A and B be situated so that C is on the Imaginary axis?

How should A and B be situated so that C is at the Origin?

Complex numbers are often represented by a vector, a ray that connects the origin to the complex point. If you can imagine completing the quadrilateral OACB (with O being the origin), what kind of special quadrilateral would you create? Keep moving the points around until you convince yourself of that fact.

We can multiply complex numbers by a scalar (a real number.) For example: 2(4-5i)=8-10i. Set point B to -3+2i. What would point A have to be for point C to be 3(-3+2i)? What is interesting about the arrangement of A, B and C? Why does that make some sense/what geometric transformation is the same as multiplying a complex number by a scalar?