Convert point from a plane to another

Question

I have two planes:

• Plane A $[x,y]$
• Plane B $[x,y]$

$[0,0]$ of $A$ is on $[0,0]$ of $B$. However, the axis $x$ of plan A doesn't have the same angle than the one of B. I have the angle of B, and the angle of A, so I know the difference. I have a point $p$ with coordinates on $B$. This point is on $A$ too, but how can I know the coordinates of $p$ on $A$?

Answer 1

If $A$ is transformed to $B$ by a trigonometric rotation of angle $\theta$, the coordinate transformation is best described in complex numbers,

$$z_B=e^{i\theta}z_A.$$