How is multiplying 3 - 2i by i^{2} represented on the complex plane?

The complex number 3 - 2i lies in _____ of the complex plane. When any complex number is multiplied by the imaginary unit, the complex number undergoes a 90° rotation in a counterclockwise direction. This means that the complex product of 3 - 2i and i^{2} lies in ______ of the complex plane.

Fill in the blank options:

quadrant I, quadrant II, quadrant III, quadrant IV

**I'm pretty positive I could figure this out if I had it graphed, but I have no idea how to graph this.. if someone could help, I'd appreciate it. I need major help here. I'm struggling really bad:(**

auxiarc May 14, 2020

#1**+2 **

(3 - 2i) ( i^2) =

(3 - 2i) (-1) =

-3 + 2i

Ignoring the imaginary part (consider that the y axis is the imaginary axis), look at the graph here : https://www.desmos.com/calculator/ks69hcjdhx

(3, -2i) lies in Quad 4

So multiplying this by i rotates it 90° counter-clockwise and multiplying this result by i again rotates it by 90° counter-clockwise once more....so....we end up in Quad 2 ⇒ (-3 + 2i) = (-3, 2i)

CPhill May 14, 2020