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Complex numbers can be thought of as polynomials of degree at most one in i.

To print polynomial expressions in some quantity, two common choices are to order by increasing or by decreasing powers of that quantity.

The choice made in Sage is usually by decreasing powers, which is at odds with the usage of writing complex numbers with real component first and imaginary component second.

Power series are another family of structures whose elements involve combinations of powers of a variable, but which, in Sage, are printed by ascending powers of the variables.

Here is a little function for printing complex numbers in our usual order, taking advantage of that.

def cprint(z):
    r"""
    Print this complex number as `a + b*i` instead of `b*I + a`.

    EXAMPLES:

        sage: aa = [2 + 3*i, -1/2 + sqrt(3)/2*i, (1+sqrt(5))/2 + (1+sqrt(5))/2*i]
        sage: for a in aa:
        ....:     cprint(a)
    """
    v = vector([z.real(), z.imag()])
    R = v.base_ring()
    print(R[['i']](v.list()))

It would be easy to tweak so it

• returns a string instead of printing it
• optionally provides a LaTeX form

Examples:

sage: aa = [2 + 3*i, -1/2 + sqrt(3)/2*i, (1+sqrt(5))/2 + (1+sqrt(5))/2*i]

sage: for a in aa:
....:     cprint(a)

2 + 3*i
-1/2 + 1/2*sqrt(3)*i
1/2*sqrt(5) + 1/2 + (1/2*sqrt(5) + 1/2)*i

Complex numbers can be thought of as polynomials of degree at most one in i.

To print polynomial expressions in some quantity, two common choices are to order by increasing or by decreasing powers of that quantity.

The choice made in Sage is usually by decreasing powers, which is at odds with the usage of writing complex numbers with real component first and imaginary component second.

Power series are another family of structures whose elements involve combinations of powers of a variable, but which, in Sage, are printed by ascending powers of the variables.

Here is a little function for printing complex numbers in our usual order, taking advantage of that.

def cprint(z):
    r"""
    Print this complex number as `a + b*i` instead of `b*I + a`.

    EXAMPLES:

        sage: aa = [2 + 3*i, -1/2 + sqrt(3)/2*i, (1+sqrt(5))/2 + (1+sqrt(5))/2*i]
        sage: for a in aa:
        ....:     cprint(a)
    """
    v = vector([z.real(), z.imag()])
    R = v.base_ring()
    print(R[['i']](v.list()))

It (It would be easy to tweak so it

• returns to return a string instead of printing it
• it, and to optionally provides provide a LaTeX form

Examples:

sage: aa = [2 + 3*i, u = 2 + 3*i
sage: print(u); cprint(u)
3*I + 2
2 + 3*i

sage: v = -1/2 + sqrt(3)/2*i, sqrt(3)/2*i
sage: print(v); cprint(v)
1/2*I*sqrt(3) - 1/2
-1/2 + 1/2*sqrt(3)*i

sage: w = (1+sqrt(5))/2 + (1+sqrt(5))/2*i]

sage: for a in aa:
....:     cprint(a)

2 + 3*i
-1/2 + 1/2*sqrt(3)*i
(1+sqrt(5))/2*i
sage: print(w); cprint(w)
(1/2*I + 1/2)*sqrt(5) + 1/2*I + 1/2
1/2*sqrt(5) + 1/2 + (1/2*sqrt(5) + 1/2)*i