# complex {base}

Complex Vectors
Package:
base
Version:
R 3.0.2

### Description

Basic functions which support complex arithmetic in R.

### Usage

```complex(length.out = 0, real = numeric(), imaginary = numeric(),
modulus = 1, argument = 0)
as.complex(x, ...)
is.complex(x)

Re(z)
Im(z)
Mod(z)
Arg(z)
Conj(z)
```

### Arguments

length.out
numeric. Desired length of the output vector, inputs being recycled as needed.
real
numeric vector.
imaginary
numeric vector.
modulus
numeric vector.
argument
numeric vector.
x
an object, probably of mode `complex`.
z
an object of mode `complex`, or one of a class for which a methods has been defined.
...
further arguments passed to or from other methods.

### Details

Complex vectors can be created with `complex`. The vector can be specified either by giving its length, its real and imaginary parts, or modulus and argument. (Giving just the length generates a vector of complex zeroes.)

`as.complex` attempts to coerce its argument to be of complex type: like `as.vector` it strips attributes including names. All forms of `NA` and `NaN` are coerced to a complex `NA`, for which both the real and imaginary parts are `NA`.

Note that `is.complex` and `is.numeric` are never both `TRUE`.

The functions `Re`, `Im`, `Mod`, `Arg` and `Conj` have their usual interpretation as returning the real part, imaginary part, modulus, argument and complex conjugate for complex values. The modulus and argument are also called the polar coordinates. If z = x + i y with real x and y, for r = Mod(z) = √(x^2 + y^2), and φ = Arg(z), x = r*cos(φ) and y = r*sin(φ). They are all internal generic primitive functions: methods can be defined for them individually or via the `Complex` group generic.

In addition, the elementary trigonometric, logarithmic, exponential, square root and hyperbolic functions are implemented for complex values.

Internally, complex numbers are stored as a pair of double precision numbers, either or both of which can be `NaN` or plus or minus infinity.

### S4 methods

`as.complex` is primitive and can have S4 methods set.

`Re`, `Im`, `Mod`, `Arg` and `Conj` constitute the S4 group generic `Complex` and so S4 methods can be set for them individually or via the group generic.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

### Examples

```require(graphics)

0i ^ (-3:3)

matrix(1i^ (-6:5), nrow = 4) #- all columns are the same
0 ^ 1i # a complex NaN

## create a complex normal vector
z <- complex(real = stats::rnorm(100), imaginary = stats::rnorm(100))
## or also (less efficiently):
z2 <- 1:2 + 1i*(8:9)

## The Arg(.) is an angle:
zz <- (rep(1:4, len = 9) + 1i*(9:1))/10
zz.shift <- complex(modulus = Mod(zz), argument = Arg(zz) + pi)
plot(zz, xlim = c(-1,1), ylim = c(-1,1), col = "red", asp = 1,
main = expression(paste("Rotation by "," ", pi == 180^o)))
abline(h = 0, v = 0, col = "blue", lty = 3)
points(zz.shift, col = "orange")```

Documentation reproduced from R 3.0.2. License: GPL-2.