Complex numbers in R

We sometimes encounter the situations of using complex numbers in our computation. For example, the square root of -1 can be denoted as 1*i. Complex numbers are implemented in the "base" package, it’s very easy to work with them. To construct a complex number x + iy, you use complex and specify its real and imaginary components explicitly as follows:

> x <- 2

> y <- 3

> z1 <- complex(real = x, imaginary = y)

> z1

[1] 2+3i

You can convert other objects to class "complex" using as.complex and test if an object is complex with is.comple

> z2 <- as.complex(-5)
> z2
[1] -5+0i
> is.complex(z2)
[1] TRUE

There are five basic mathematical operations that works on complex numbers, Re, Im, Mod, Arg, and Conj. First, you may want to extract the real and imaginary components of a complex number. You can do this using Re and Im, respectively. You can also find the modulus and complex argument of a complex number with Mod and Arg. Finally, you can take the complex conjugate of a complex number with the help of Conj.

> z3 <- complex(real = 1.3, imaginary = 6) 

> z3

[1] 1.3+6i

> Re(z3)

[1] 1.3

> Im(z3)

[1] 6

> Mod(z3)

[1] 6.139218

> Arg(z3)

[1] 1.357428

> Conj(z3)

[1] 1.3-6i