diff --git a/NEWS.md b/NEWS.md
index d3a5986905af1..a7004d6aba73b 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -325,6 +325,8 @@ Library improvements
   * The function `randn` now accepts complex arguments (`Complex{T <: AbstractFloat}`)
     ([#21973]).
 
+  * `parse(Complex{T}, string)` can parse complex numbers in common formats ([#24713]).
+
   * The function `rand` can now pick up random elements from strings, associatives
     and sets ([#22228], [#21960], [#18155], [#22224]).
 
diff --git a/base/mpfr.jl b/base/mpfr.jl
index 3048657ee59d3..8bff353fdca7f 100644
--- a/base/mpfr.jl
+++ b/base/mpfr.jl
@@ -125,6 +125,7 @@ convert(::Type{BigFloat}, x::Union{Float16,Float32}) = BigFloat(Float64(x))
 convert(::Type{BigFloat}, x::Rational) = BigFloat(numerator(x)) / BigFloat(denominator(x))
 
 function tryparse(::Type{BigFloat}, s::AbstractString, base::Int=0)
+    !isempty(s) && isspace(s[end]) && return tryparse(BigFloat, rstrip(s), base)
     z = BigFloat()
     err = ccall((:mpfr_set_str, :libmpfr), Int32, (Ref{BigFloat}, Cstring, Int32, Int32), z, s, base, ROUNDING_MODE[])
     err == 0 ? Nullable(z) : Nullable{BigFloat}()
diff --git a/base/parse.jl b/base/parse.jl
index d4fbff975321d..87447ba0a0a90 100644
--- a/base/parse.jl
+++ b/base/parse.jl
@@ -7,9 +7,12 @@ import Base.Checked: add_with_overflow, mul_with_overflow
 """
     parse(type, str, [base])
 
-Parse a string as a number. If the type is an integer type, then a base can be specified
-(the default is 10). If the type is a floating point type, the string is parsed as a decimal
-floating point number. If the string does not contain a valid number, an error is raised.
+Parse a string as a number. For `Integer` types, a base can be specified
+(the default is 10). For floating-point types, the string is parsed as a decimal
+floating-point number.  `Complex` types are parsed from decimal strings
+of the form `"R±Iim"` as a `Complex(R,I)` of the requested type; `"i"` or `"j"` can also be
+used instead of `"im"`, and `"R"` or `"Iim"` are also permitted.
+If the string does not contain a valid number, an error is raised.
 
 ```jldoctest
 julia> parse(Int, "1234")
@@ -23,6 +26,9 @@ julia> parse(Int, "afc", 16)
 
 julia> parse(Float64, "1.2e-3")
 0.0012
+
+julia> parse(Complex{Float64}, "3.2e-1 + 4.5im")
+0.32 + 4.5im
 ```
 """
 parse(T::Type, str, base=Int)
@@ -151,7 +157,7 @@ function tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::
     return Nullable{T}(n)
 end
 
-function tryparse_internal(::Type{Bool}, sbuff::Union{String,SubString},
+function tryparse_internal(::Type{Bool}, sbuff::Union{String,SubString{String}},
         startpos::Int, endpos::Int, base::Integer, raise::Bool)
     if isempty(sbuff)
         raise && throw(ArgumentError("input string is empty"))
@@ -215,24 +221,98 @@ function parse(::Type{T}, s::AbstractString) where T<:Integer
     get(tryparse_internal(T, s, start(s), endof(s), 0, true)) # Zero means, "figure it out"
 end
 
-
 ## string to float functions ##
 
 tryparse(::Type{Float64}, s::String) = ccall(:jl_try_substrtod, Nullable{Float64}, (Ptr{UInt8},Csize_t,Csize_t), s, 0, sizeof(s))
 tryparse(::Type{Float64}, s::SubString{String}) = ccall(:jl_try_substrtod, Nullable{Float64}, (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset, s.endof)
+tryparse_internal(::Type{Float64}, s::String, startpos::Int, endpos::Int) = ccall(:jl_try_substrtod, Nullable{Float64}, (Ptr{UInt8},Csize_t,Csize_t), s, startpos-1, endpos-startpos+1)
+tryparse_internal(::Type{Float64}, s::SubString{String}, startpos::Int, endpos::Int) = ccall(:jl_try_substrtod, Nullable{Float64}, (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset+startpos-1, endpos-startpos+1)
 
 tryparse(::Type{Float32}, s::String) = ccall(:jl_try_substrtof, Nullable{Float32}, (Ptr{UInt8},Csize_t,Csize_t), s, 0, sizeof(s))
 tryparse(::Type{Float32}, s::SubString{String}) = ccall(:jl_try_substrtof, Nullable{Float32}, (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset, s.endof)
+tryparse_internal(::Type{Float32}, s::String, startpos::Int, endpos::Int) = ccall(:jl_try_substrtof, Nullable{Float32}, (Ptr{UInt8},Csize_t,Csize_t), s, startpos-1, endpos-startpos+1)
+tryparse_internal(::Type{Float32}, s::SubString{String}, startpos::Int, endpos::Int) = ccall(:jl_try_substrtof, Nullable{Float32}, (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset+startpos-1, endpos-startpos+1)
 
 tryparse(::Type{T}, s::AbstractString) where {T<:Union{Float32,Float64}} = tryparse(T, String(s))
 
 tryparse(::Type{Float16}, s::AbstractString) = convert(Nullable{Float16}, tryparse(Float32, s))
+tryparse_internal(::Type{Float16}, s::AbstractString, startpos::Int, endpos::Int) =
+    convert(Nullable{Float16}, tryparse_internal(Float32, s, startpos, endpos))
+
+## string to complex functions ##
+
+function tryparse_internal(::Type{Complex{T}}, s::Union{String,SubString{String}}, i::Int, e::Int, raise::Bool) where {T<:Real}
+    # skip initial whitespace
+    while i ≤ e && isspace(s[i])
+        i = nextind(s, i)
+    end
+    if i > e
+        raise && throw(ArgumentError("input string is empty or only contains whitespace"))
+        return Nullable{Complex{T}}()
+    end
+
+    # find index of ± separating real/imaginary parts (if any)
+    i₊ = search(s, ('+','-'), i)
+    if i₊ == i # leading ± sign
+        i₊ = search(s, ('+','-'), i₊+1)
+    end
+    if i₊ != 0 && s[i₊-1] in ('e','E') # exponent sign
+        i₊ = search(s, ('+','-'), i₊+1)
+    end
+
+    # find trailing im/i/j
+    iᵢ = rsearch(s, ('m','i','j'), e)
+    if iᵢ > 0 && s[iᵢ] == 'm' # im
+        iᵢ -= 1
+        if s[iᵢ] != 'i'
+            raise && throw(ArgumentError("expected trailing \"im\", found only \"m\""))
+            return Nullable{Complex{T}}()
+        end
+    end
+
+    if i₊ == 0 # purely real or imaginary value
+        if iᵢ > 0 # purely imaginary
+            x_ = tryparse_internal(T, s, i, iᵢ-1, raise)
+            isnull(x_) && return Nullable{Complex{T}}()
+            x = unsafe_get(x_)
+            return Nullable{Complex{T}}(Complex{T}(zero(x),x))
+        else # purely real
+            return Nullable{Complex{T}}(tryparse_internal(T, s, i, e, raise))
+        end
+    end
+
+    if iᵢ < i₊
+        raise && throw(ArgumentError("missing imaginary unit"))
+        return Nullable{Complex{T}}() # no imaginary part
+    end
+
+    # parse real part
+    re = tryparse_internal(T, s, i, i₊-1, raise)
+    isnull(re) && return Nullable{Complex{T}}()
+
+    # parse imaginary part
+    im = tryparse_internal(T, s, i₊+1, iᵢ-1, raise)
+    isnull(im) && return Nullable{Complex{T}}()
+
+    return Nullable{Complex{T}}(Complex{T}(unsafe_get(re), s[i₊]=='-' ? -unsafe_get(im) : unsafe_get(im)))
+end
 
-function parse(::Type{T}, s::AbstractString) where T<:AbstractFloat
-    result = tryparse(T, s)
-    if isnull(result)
-        throw(ArgumentError("cannot parse $(repr(s)) as $T"))
+# the ±1 indexing above for ascii chars is specific to String, so convert:
+tryparse_internal(T::Type{<:Complex}, s::AbstractString, i::Int, e::Int, raise::Bool) =
+    tryparse_internal(T, String(s), i, e, raise)
+
+# fallback methods for tryparse_internal
+tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int) where T<:Real =
+    startpos == start(s) && endpos == endof(s) ? tryparse(T, s) : tryparse(T, SubString(s, startpos, endpos))
+function tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int, raise::Bool) where T<:Real
+    result = tryparse_internal(T, s, startpos, endpos)
+    if raise && isnull(result)
+        throw(ArgumentError("cannot parse $(repr(s[startpos:endpos])) as $T"))
     end
-    return unsafe_get(result)
+    return result
 end
+tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int, raise::Bool) where T<:Integer =
+    tryparse_internal(T, s, startpos, endpos, 10, raise)
 
+parse(::Type{T}, s::AbstractString) where T<:Union{Real,Complex} =
+    unsafe_get(tryparse_internal(T, s, start(s), endof(s), true))
diff --git a/stdlib/DelimitedFiles/src/DelimitedFiles.jl b/stdlib/DelimitedFiles/src/DelimitedFiles.jl
index 9326ac78938db..964bec6e98dac 100644
--- a/stdlib/DelimitedFiles/src/DelimitedFiles.jl
+++ b/stdlib/DelimitedFiles/src/DelimitedFiles.jl
@@ -393,22 +393,17 @@ end
 
 function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{Bool,2}, row::Int, col::Int)
     n = tryparse_internal(Bool, sbuff, startpos, endpos, 0, false)
-    isnull(n) || (cells[row, col] = get(n))
+    isnull(n) || (cells[row, col] = unsafe_get(n))
     isnull(n)
 end
 function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{T,2}, row::Int, col::Int) where T<:Integer
     n = tryparse_internal(T, sbuff, startpos, endpos, 0, false)
-    isnull(n) || (cells[row, col] = get(n))
+    isnull(n) || (cells[row, col] = unsafe_get(n))
     isnull(n)
 end
-function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{Float64,2}, row::Int, col::Int)
-    n = ccall(:jl_try_substrtod, Nullable{Float64}, (Ptr{UInt8},Csize_t,Csize_t), sbuff, startpos-1, endpos-startpos+1)
-    isnull(n) || (cells[row, col] = get(n))
-    isnull(n)
-end
-function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{Float32,2}, row::Int, col::Int)
-    n = ccall(:jl_try_substrtof, Nullable{Float32}, (Ptr{UInt8}, Csize_t, Csize_t), sbuff, startpos-1, endpos-startpos+1)
-    isnull(n) || (cells[row, col] = get(n))
+function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{T,2}, row::Int, col::Int) where T<:Union{Real,Complex}
+    n = tryparse_internal(T, sbuff, startpos, endpos, false)
+    isnull(n) || (cells[row, col] = unsafe_get(n))
     isnull(n)
 end
 function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{<:AbstractString,2}, row::Int, col::Int)
@@ -421,15 +416,15 @@ function colval(sbuff::String, startpos::Int, endpos::Int, cells::Array{Any,2},
     if len > 0
         # check Inteter
         ni64 = tryparse_internal(Int, sbuff, startpos, endpos, 0, false)
-        isnull(ni64) || (cells[row, col] = get(ni64); return false)
+        isnull(ni64) || (cells[row, col] = unsafe_get(ni64); return false)
 
         # check Bool
         nb = tryparse_internal(Bool, sbuff, startpos, endpos, 0, false)
-        isnull(nb) || (cells[row, col] = get(nb); return false)
+        isnull(nb) || (cells[row, col] = unsafe_get(nb); return false)
 
         # check float64
         nf64 = ccall(:jl_try_substrtod, Nullable{Float64}, (Ptr{UInt8}, Csize_t, Csize_t), sbuff, startpos-1, endpos-startpos+1)
-        isnull(nf64) || (cells[row, col] = get(nf64); return false)
+        isnull(nf64) || (cells[row, col] = unsafe_get(nf64); return false)
     end
     cells[row, col] = SubString(sbuff, startpos, endpos)
     false
diff --git a/stdlib/DelimitedFiles/test/runtests.jl b/stdlib/DelimitedFiles/test/runtests.jl
index f41bd7d0728fa..092f6aa87f815 100644
--- a/stdlib/DelimitedFiles/test/runtests.jl
+++ b/stdlib/DelimitedFiles/test/runtests.jl
@@ -290,3 +290,7 @@ let d = TextDisplay(IOBuffer())
     display(d, "text/csv", [3 1 4])
     @test String(take!(d.io)) == "3,1,4\n"
 end
+
+@testset "complex" begin
+    @test readdlm(IOBuffer("3+4im, 4+5im"), ',', Complex{Int}) == [3+4im 4+5im]
+end
diff --git a/test/mpfr.jl b/test/mpfr.jl
index 5dc38118ae3f9..2c73f7e6ea7d2 100644
--- a/test/mpfr.jl
+++ b/test/mpfr.jl
@@ -7,22 +7,10 @@ import Base.MPFR
         x = BigFloat(12)
     end
     x = BigFloat(12)
-    y = BigFloat(x)
-    @test x ≈ y
-    y = BigFloat(0xc)
-    @test x ≈ y
-    y = BigFloat(12.)
-    @test x ≈ y
-    y = BigFloat(BigInt(12))
-    @test x ≈ y
-    y = BigFloat(BigFloat(12))
-    @test x ≈ y
-    y = parse(BigFloat,"12")
-    @test x ≈ y
-    y = BigFloat(Float32(12.))
-    @test x ≈ y
-    y = BigFloat(12//1)
-    @test x ≈ y
+    @test x == BigFloat(x) == BigFloat(0xc) == BigFloat(12.) ==
+          BigFloat(BigInt(12)) == BigFloat(BigFloat(12)) == parse(BigFloat,"12") ==
+          parse(BigFloat,"12 ") == parse(BigFloat," 12") == parse(BigFloat," 12 ") ==
+          BigFloat(Float32(12.)) == BigFloat(12//1)
 
     @test typeof(BigFloat(typemax(Int8))) == BigFloat
     @test typeof(BigFloat(typemax(Int16))) == BigFloat
diff --git a/test/parse.jl b/test/parse.jl
index e338020bf0f72..2792058e18237 100644
--- a/test/parse.jl
+++ b/test/parse.jl
@@ -229,3 +229,28 @@ end
 @test tryparse(Float32, "1.23") === Nullable(1.23f0)
 @test tryparse(Float16, "1.23") === Nullable(Float16(1.23))
 
+# parsing complex numbers (#22250)
+@testset "complex parsing" begin
+    for r in (1,0,-1), i in (1,0,-1), sign in ('-','+'), Im in ("i","j","im")
+        for s1 in (""," "), s2 in (""," "), s3 in (""," "), s4 in (""," ")
+            n = Complex(r, sign == '+' ? i : -i)
+            s = string(s1, r, s2, sign, s3, i, Im, s4)
+            @test n === parse(Complex{Int}, s)
+            @test Complex(r) === parse(Complex{Int}, string(s1, r, s2))
+            @test Complex(0,i) === parse(Complex{Int}, string(s3, i, Im, s4))
+            for T in (Float64, BigFloat)
+                nT = parse(Complex{T}, s)
+                @test nT isa Complex{T}
+                @test nT == n
+                @test n == parse(Complex{T}, string(s1, r, ".0", s2, sign, s3, i, ".0", Im, s4))
+                @test n*parse(T,"1e-3") == parse(Complex{T}, string(s1, r, "e-3", s2, sign, s3, i, "e-3", Im, s4))
+            end
+        end
+    end
+    @test parse(Complex{Float16}, "3.3+4i") === Complex{Float16}(3.3+4im)
+    @test parse(Complex{Int}, SubString("xxxxxx1+2imxxxx", 7, 10)) === 1+2im
+    for T in (Int, Float64), bad in ("3 + 4*im", "3 + 4", "1+2ij", "1im-3im", "++4im")
+        @test_throws ArgumentError parse(Complex{T}, bad)
+    end
+    @test_throws ArgumentError parse(Complex{Int}, "3 + 4.2im")
+end