The number i is a pure imaginary number. The arithmetic with complex numbers is straightforward. It follows that the addition of two complex numbers is a vectorial addition. In other words, it's the projection of the vector onto the x and y axes. Mathematicians call rho the norm or modulus and theta the argument of the complex number.
Real numbers are on the x axis, and therefore theta is zero or pi .
All the common operations that can be performed on a real number have been defined to work on complex numbers as well, and are merely extensions of the operations defined on real numbers. This means they keep their natural meaning when there is no imaginary part, provided the number is within their definition set. This justifies a posteriori our use of the abs notation for the norm. Re , Im , arg , abs , rho , and theta can be used also also mutators. The root function is available to compute all the n roots of some complex, where n is a strictly positive integer.