complex(length.out = 0, real = numeric(), imaginary = numeric(),
modulus = 1, argument = 0)
as.complex(z)
is.complex(z)
Re(z)
Im(z)
Mod(z)
Arg(z)
Conj(z)
complex. The vector can be
specified either by giving its length, its real and imaginary parts, or
modulus and argument.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,
Mod(z) = sqrt{x^2 + y^2}, and for
phi= Arg(z), x = cos(phi) and y = sin(phi).
In addition, the elementary trigonometric, logarithmic and exponential functions are available for complex values.
( z <- 0i ^ (-3:3) )
all(Re(z) == 0 ^ (-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)
all(Mod ( 1 - sin(z) / ( (exp(1i*z)-exp(-1i*z))/(2*1i) ))
< 100*.Machine$double.eps)
## 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")