- (make-rectangular x x)procedure
- (make-polar x x)procedure
- real-part zprocedure
- imag-part zprocedure
- magnitude zprocedure
- angle zprocedure
These procedures are part of every implementation that supports general complex numbers. Suppose x, x, x, and x are real numbers and z is a complex number such that
z = x + xi = x . e^i x
(make-rectangular x x) ===> z (make-polar x x) ===> z (real-part z) ===> x (imag-part z) ===> x (magnitude z) ===> |x| (angle z) ===> x[angle]
where - pi < x[angle] < pi with x[angle] = x + 2 pi n for some integer n.
Rationale: Magnitude is the same as abs for a real argument, but abs must be present in all implementations, whereas magnitude need only be present in implementations that support general complex numbers.