complex {base} | R Documentation |

## Complex Vectors

### 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. Modulus and argument are also called the *polar
coordinates*. If *z = x + i y* with real *x* and *y*,
for *r = *`Mod`

(z) = sqrt{x^2 + y^2}, and
*phi = *`Arg`

(z), *x = r*cos(phi)* and
*y = r*sin(phi)*.
They are all generic functions: methods can be defined
for them individually or via the `Complex`

group generic.

In addition, the elementary trigonometric, logarithmic and exponential
functions are available for complex values.

### References

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

### Examples

0i ^ (-3:3)
matrix(1i^ (-6:5), nr=4)#- all columns are the same
0 ^ 1i # a complex NaN
## create a complex normal vector
z <- complex(real = rnorm(100), imag = 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")

[Package

*base* version 2.5.0

Index]