diff --git a/base/complex.jl b/base/complex.jl
index 0d985dd49155c..eb5dbb2fbe629 100644
--- a/base/complex.jl
+++ b/base/complex.jl
@@ -351,19 +351,7 @@ muladd(z::Complex, w::Complex, x::Real) =
     Complex(muladd(real(z), real(w), -muladd(imag(z), imag(w), -x)),
             muladd(real(z), imag(w), imag(z) * real(w)))
 
-function /(a::R, z::S) where {R<:Real, S<:Complex}
-    T = promote_type(R,S)
-    z_p = T(z)
-    if z_p isa Complex{<:Rational}
-        # avoid overflow if a is zero and z isn't zero
-        if iszero(z_p)
-            throw(DivideError())
-        elseif iszero(a)
-            return a*inv(oneunit(z_p))
-        end
-    end
-    a*inv(z_p)
-end
+/(a::R, z::S) where {R<:Real, S<:Complex} = (T = promote_type(R,S); a*inv(T(z)))
 /(z::Complex, x::Real) = Complex(real(z)/x, imag(z)/x)
 
 function /(a::Complex{T}, b::Complex{T}) where T<:Real
diff --git a/base/rational.jl b/base/rational.jl
index 6b54a409588d2..3736173cc3626 100644
--- a/base/rational.jl
+++ b/base/rational.jl
@@ -403,6 +403,18 @@ function *(y::Integer, x::Rational)
 end
 /(x::Rational, y::Union{Rational, Integer}) = x//y
 /(x::Integer, y::Rational) = x//y
+# Avoid overflow for Rational math if result is zero.
+# This method is needed because previously this method didn't check for overflows
+# but would return the correct answer if `a` was zero even if 1//z was wrong.
+function /(a::Rational, z::Complex{<:Integer})
+    z_r = complex(Rational(real(z)), Rational(imag(z)))
+    if iszero(a) && !iszero(z)
+        a/oneunit(z_r)
+    else
+        a/z_r
+    end
+end
+
 inv(x::Rational) = checked_den(x.den, x.num)
 
 fma(x::Rational, y::Rational, z::Rational) = x*y+z
diff --git a/test/rational.jl b/test/rational.jl
index 548d3b9f0295e..59d21aede7fd6 100644
--- a/test/rational.jl
+++ b/test/rational.jl
@@ -203,15 +203,19 @@ end
     end
 
     @test Rational(rand_int, 3)/Complex(3, 2) == Complex(Rational(rand_int, 13), -Rational(rand_int*2, 39))
-    @test iszero(zero(Rational{Int8}) / complex(Rational{Int8}(100), Rational{Int8}(100)))
-    @test iszero(zero(Int8) / complex(Rational{Int8}(100), Rational{Int8}(100)))
     @test iszero(zero(Rational{Int8}) / complex(Int8(100), Int8(100)))
+    @test (true//true) / complex(false, true) === 0//1 - 1//1*im
+    @test (false//true) / complex(false, true) === 0//1 + 0//1*im
+    @test (false//true) / complex(true, false) === 0//1 + 0//1*im
     @test (false//true) / complex(true, true) === 0//1 + 0//1*im
     @test (true//true) / complex(true, true) === 1//2 - 1//2*im
     @test (false//true) / complex(true//true, true//true) === 0//1 + 0//1*im
     @test (true//true) / complex(true//true, true//true) === 1//2 - 1//2*im
     @test (false//true) / complex(true//false, false//true) === 0//1 + 0//1*im
     @test (true//true) / complex(true//true, true//false) === 0//1 + 0//1*im
+    @test_throws DivideError (0//1) / complex(0, 0)
+    @test_throws DivideError (1//1) / complex(0, 0)
+    @test_throws DivideError (1//0) / complex(0, 0)
 
     # 1//200 - 1//200*im cannot be represented as Complex{Rational{Int8}}
     @test_throws OverflowError (Int8(1)//Int8(1)) / (Int8(100) + Int8(100)im)