complex {base}R Documentation

Complex Vectors


Basic functions which support complex arithmetic in R.


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



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.


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.


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


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]