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\details{
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\details{
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Complex vectors can be created with \code{complex}. The vector can be
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Complex vectors can be created with \code{complex}. The vector can be
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specified either by giving its length, its real and imaginary parts, or
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specified either by giving its length, its real and imaginary parts, or
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modulus and argument. (Giving just the length generates a vector of
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modulus and argument. (Giving just the length generates a vector of
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complex zeroes.)
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complex zeroes.)
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\code{as.complex} attempts to coerce its argument to be of complex
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\code{as.complex} attempts to coerce its argument to be of complex
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type: like \code{\link{as.vector}} it strips attributes including names.
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type: like \code{\link{as.vector}} it strips attributes including names.
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Note that \code{is.complex} and \code{is.numeric} are never both
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Note that \code{is.complex} and \code{is.numeric} are never both
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\code{TRUE}.
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\code{TRUE}.
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The functions \code{Re}, \code{Im}, \code{Mod}, \code{Arg} and
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The functions \code{Re}, \code{Im}, \code{Mod}, \code{Arg} and
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\code{Conj} have their usual interpretation as returning the real
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\code{Conj} have their usual interpretation as returning the real
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part, imaginary part, modulus, argument and complex conjugate for
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part, imaginary part, modulus, argument and complex conjugate for
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complex values. Modulus and argument are also called the \emph{polar
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complex values. Modulus and argument are also called the \emph{polar
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coordinates}. If \eqn{z = x + i y} with real \eqn{x} and \eqn{y},
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coordinates}. If \eqn{z = x + i y} with real \eqn{x} and \eqn{y},
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\code{Mod}\eqn{(z) = \sqrt{x^2 + y^2}}, and for
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for \eqn{r = \code{Mod}(z) = \sqrt{x^2 + y^2}}, and
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\eqn{\phi= \code{Arg}(z)}, \eqn{x = \code{Mod}(z)\cos(\phi)} and
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\eqn{\phi = \code{Arg}(z)}, \eqn{x = r*\cos(\phi)} and \eqn{y = r*\sin(\phi)}.
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\eqn{y = \code{Mod}(z)\sin(\phi)}.
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They are all generic functions: methods can be defined
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They are all generic functions: methods can be defined
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for them individually or via the \code{\link{Complex}} group generic.
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for them individually or via the \code{\link{Complex}} group generic.
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In addition, the elementary trigonometric, logarithmic and exponential
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In addition, the elementary trigonometric, logarithmic and exponential
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functions are available for complex values.
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functions are available for complex values.
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