### R complex Function

`complex()` function do complex number calculations.

```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)
```

`length.out`: numeric. Desired length of the output vector, inputs being recycled as needed
`real`: numeric vector
`imaginary`: numeric vector
`modulus`: numberic vector
`argument`:
`x, z`: complex object
`...`

```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")
```