Question

What is the rotation of point A (-2, 3). 90 degrees?

A. (2,3)
B. (-2,-3)
C. (3,-2)
D. (3,-2)

Answer 1

Explanation:

Let's pretend our point is actually a complex number. That would make the point -2–3i. Why would we do this? Well, rotation of complex numbers is simply a matter of multiplication, in this case by 1∠−90° , or -i.

So to start, you shift the point of rotation to 0+0i, rotate it by multiplying, then shift it back to the axis of rotation.

z=−i[(−2−x0)+(−3−y0)i]+(x0+iy0)

=−3−y0+x0+(2+x0+y0)i

x=Rz

y=Iz

Thus the new point is at (−3+x0−y0,2+x0+y0)

hence (-3,2)