How to calculate rotation of a point

1. How do you rotate a point by 45 degrees?
2. How do you rotate a point by 90?

How do you rotate a point by 45 degrees?

If we represent the point (x,y) by the complex number x+iy, then we can rotate it 45 degrees clockwise simply by multiplying by the complex number (1−i)/√2 and then reading off their x and y coordinates.

How do you rotate a point by 90?

The rule for a rotation by 90° about the origin is (x,y)→(−y,x) .