Maxwell's equations in vector notation are often cited as a prime example of the beauty of physics, but the elegance is only enhanced in geometric algebra.

Vector notation A vector quantity has both direction and magnitude . (In contrast a scalar quantity has magnitude only - eg, the numbers 1, 2, 3, 4...) The diagram above represents a vector.

Without vector notation, this would be written as three separate equations (one for each component of B and E) — each one a tangle of coordinates, multiplications and subtractions.

Complex numbers have the interpretation of vectors that rotate in the complex plane. This interpretation can be extended to represent complex numbers as two dimensional vectors using standard vector ...