diff --git a/base/parse.jl b/base/parse.jl
index f6a93e56369b7..ab1adb7c30895 100644
--- a/base/parse.jl
+++ b/base/parse.jl
@@ -321,14 +321,14 @@ function tryparse_internal(::Type{Complex{T}}, s::Union{String,SubString{String}
     if i₊ == i # leading ± sign
         i₊ = something(findnext(in(('+','-')), s, i₊+1), 0)
     end
-    if i₊ != 0 && s[i₊-1] in ('e','E') # exponent sign
+    if i₊ != 0 && s[prevind(s, i₊)] in ('e','E') # exponent sign
         i₊ = something(findnext(in(('+','-')), s, i₊+1), 0)
     end
 
     # find trailing im/i/j
     iᵢ = something(findprev(in(('m','i','j')), s, e), 0)
     if iᵢ > 0 && s[iᵢ] == 'm' # im
-        iᵢ -= 1
+        iᵢ = prevind(s, iᵢ)
         if s[iᵢ] != 'i'
             raise && throw(ArgumentError("expected trailing \"im\", found only \"m\""))
             return nothing
@@ -337,7 +337,7 @@ function tryparse_internal(::Type{Complex{T}}, s::Union{String,SubString{String}
 
     if i₊ == 0 # purely real or imaginary value
         if iᵢ > i && !(iᵢ == i+1 && s[i] in ('+','-')) # purely imaginary (not "±inf")
-            x = tryparse_internal(T, s, i, iᵢ-1, raise)
+            x = tryparse_internal(T, s, i, prevind(s, iᵢ), raise)
             x === nothing && return nothing
             return Complex{T}(zero(x),x)
         else # purely real
@@ -353,11 +353,11 @@ function tryparse_internal(::Type{Complex{T}}, s::Union{String,SubString{String}
     end
 
     # parse real part
-    re = tryparse_internal(T, s, i, i₊-1, raise)
+    re = tryparse_internal(T, s, i, prevind(s, i₊), raise)
     re === nothing && return nothing
 
     # parse imaginary part
-    im = tryparse_internal(T, s, i₊+1, iᵢ-1, raise)
+    im = tryparse_internal(T, s, i₊+1, prevind(s, iᵢ), raise)
     im === nothing && return nothing
 
     return Complex{T}(re, s[i₊]=='-' ? -im : im)
diff --git a/test/parse.jl b/test/parse.jl
index 69092b2c4188d..e2b94a45cc446 100644
--- a/test/parse.jl
+++ b/test/parse.jl
@@ -296,6 +296,8 @@ end
         @test_throws ArgumentError parse(Complex{T}, bad)
     end
     @test_throws ArgumentError parse(Complex{Int}, "3 + 4.2im")
+    @test_throws ArgumentError parse(ComplexF64, "3 β+ 4im")
+    @test_throws ArgumentError parse(ComplexF64, "3 + 4αm")
 end
 
 @testset "parse and tryparse type inference" begin