Type-preserving (complex, real) square root in R?

Question

(Reproducible example added)

sqrt(as.complex(c(4,9,-4,-9,16))) # 2+0i 3+0i 0+2i 0+3i 4+0i
class(sqrt(as.complex(c(4,9,-4,-9,16)))) # complex
sqrt(as.complex(c(4,9,-4,-9,16)))[1] # 2+0i
class(sqrt(as.complex(c(4,9,-4,-9,16)))[1]) # complex

So, I wanna define a specific square-root function (sqrtT) that will preserve the realness/complexness of its elements. So in effect, I want this:

sqrtT(as.complex(c(4,9,-4,-9,16))) # 2 3 0+2i 0+3i 4
class(sqrtT(as.complex(c(4,9,-4,-9,16)))) # complex
sqrtT(as.complex(c(4,9,-4,-9,16)))[1] # 2
class(sqrtT(as.complex(c(4,9,-4,-9,16)))[1]) # numeric
class(sqrtT(as.complex(c(4,9,-4,-9,16)))[3]) # complex

What I did:
I found these tools:
1.

Re(sqrt(as.complex(c(4,9,-4,-9,16)))) # 2 3 0 0 4
Im(sqrt(as.complex(c(4,9,-4,-9,16)))) # 0 0 2 3 0

By the way, it must hold the type in itself, i.e., when I say, sqrtT(as.complex(c(4,9,-4,-9,16))) #= 2 3 0+2i 0+3i 4, the displaying this output (2 3 0+2i 0+3i 4) while in essence having all as complex is not what I want. My problem is not display-purpose only.

2. There is a way to distinguish the contents of the elements in the vector:

is.numeric(0+2i) # FALSE
is.numeric(2) # TRUE

3. The indices with imaginary part non-equal to 0 and equal to 0:

Let the vector be v.

v <- c(-1,4,9,-4,-9,0,16)
# The indices with imaginary part non-equal to 0 (IM<>0):
IMneq0 <- setdiff(which(as.numeric(sqrt(as.complex(v))) %in% 0),which(sqrt(as.complex(v))==0) )
IMneq0 # 1,4,5

# The indices with imaginary part equal to 0 (IM=0):
IMeq0 <- setdiff(1:length(sqrt(as.complex(v))),IMneq0 )
IMeq0 # 2 3 6 7

Auto-coercion to the complex can be by-passed through using lists.

Any idea?

Answer 1

(a bad pseudo-solution)

v <- c(-1,4,9,-4,-9,0,16)

sqrtTP <- function(v) { # Type preserving square root
IMne0 <- setdiff(which(as.numeric(sqrt(as.complex(v))) %in% 0),which(sqrt(as.complex(v))==0) )  #indices with imaginary part <> 0
IM0 <- setdiff(1:length(sqrt(as.complex(v))),IMne0 )   #indices with imaginary part =0
ValuesIM0 <- as.numeric(sqrt(as.complex(v[IM0]))) # values where IM=0
ValuesIMne0 <- sqrt(as.complex(v[IMne0])) # values where IM<>0
out <- list()
CounterIM0 <- 1 # counter where IM=0 coincided
CounterIMne0 <- 1 #  counter where IM<>0 coincided

for (i in as.integer(1:length(v))) {

if (i %in% IM0) {
out[[i]] <- ValuesIM0[CounterIM0]
CounterIM0 <- CounterIM0 +1
} else {
out[[i]] <- ValuesIMne0[CounterIMne0]
CounterIMne0 <- CounterIMne0 +1
}
}
out
}

sqrtTP(v)
# 0+1i  2   3  0+2i  0+3i   0  4  (given as list elements)