We learned that multiplying by i produces a 90° counterclockwise rotation about the origin. what do we ned to
multiply by to produce a 90° clockwise rotation about the origin?

For producing 90° rotation clockwise abut origin we have to multiply with -i

Step-by-step explanation:

We know that when we multiply with i in an number then it will give 90° counterclockwise rotation

We have to find the quantity after which it will produce 90° clockwise rotation

Generally we take counterclockwise as positive angle and clockwise as negative angle

So basically we have to produce -90° angle

For producing 90° rotation clockwise abut origin we have to multiply with -i