Triangle PDQ is congruence to triangle PSR with PR equal to unity.
Drag Q or P to approach each other and examine the congruence of the green and brown triangles.
What is the orientational relationship between the segments OP and PR?
Consider the graph is a complex plane.
The applet shows that the derivative of a unit complex number P with respect to its argument.
The derivative is equal to P rotated anti-clockwise by a right angle.
Hence, [math]. Solving for P to yield [math].