## Julia – 13 – numeri complessi e razionali – 1

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Julia ships with predefined types representing both complex and rational numbers, and supports all standard Mathematical Operations and Elementary Functions on them. Conversion and Promotion [prossimamente] are defined so that operations on any combination of predefined numeric types, whether primitive or composite, behave as expected.

Numeri complessi
The global constant `im` is bound to the complex number i, representing the principal square root of -1. It was deemed harmful to co-opt the name i for a global constant, since it is such a popular index variable name. Since Julia allows numeric literals to be juxtaposed with identifiers as coefficients, this binding suffices to provide convenient syntax for complex numbers, similar to the traditional mathematical notation:

You can perform all the standard arithmetic operations with complex numbers:

The promotion mechanism ensures that combinations of operands of different types just work:

Note that `3/4im == 3/(4*im) == -(3/4*im)`, since a literal coefficient binds more tightly than division.

Standard functions to manipulate complex values are provided:

As usual, the absolute value (`abs()`) of a complex number is its distance from zero. `abs2()` gives the square of the absolute value, and is of particular use for complex numbers where it avoids taking a square root. `angle()` returns the phase angle in radians (also known as the argument or `arg` function). The full gamut of other Elementary Functions is also defined for complex numbers:

Note that mathematical functions typically return real values when applied to real numbers and complex values when applied to complex numbers. For example, `sqrt()` behaves differently when applied to `-1` versus `-1 + 0im` even though `-1 == -1 + 0im`:

The literal numeric coefficient notation does not work when constructing a complex number from variables. Instead, the multiplication must be explicitly written out:

However, this is not recommended; Use the `complex()` function instead to construct a complex value directly from its real and imaginary parts:

This construction avoids the multiplication and addition operations.

`Inf` and `NaN` propagate through complex numbers in the real and imaginary parts of a complex number:

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