When one first learns about the complex numbers, one is taught to think of them as a two-dimensional space, with one real and one imaginary dimension: a complex number *z* = *x* + i*y* has real part *x* and imaginary part y, where i is a square root of - 1.

Now let us consider what the complex numbers that have *integers* for their real and imaginary parts look like. These complex numbers, such as 3 + 4i or -23i, form a “lattice” in the complex plane (see figure 1).

By definition, every element of this lattice is of the form *m* + *n*i for some pair of integers *m* and *n*. We say that the lattice is *generated* by 1 and i, and use the notation + i for it. Note that this lattice can be generated ...

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