diff --git a/stl/inc/complex b/stl/inc/complex
index dc9ced16f3b..97c3ddd4c67 100644
--- a/stl/inc/complex
+++ b/stl/inc/complex
@@ -1758,8 +1758,11 @@ template <class _Ty>
 using _Upgrade_to_double = conditional_t<is_integral_v<_Ty>, double, _Ty>;
 
 template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
-_NODISCARD _Upgrade_to_double<_Ty> arg(_Ty) {
-    return 0;
+_NODISCARD _Upgrade_to_double<_Ty> arg(_Ty _Left) {
+    using _Upgraded = _Upgrade_to_double<_Ty>;
+    const auto _Val = static_cast<_Upgraded>(_Left);
+
+    return _Ctraits<_Upgraded>::atan2(0, _Val);
 }
 
 template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
@@ -1769,22 +1772,40 @@ _NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> imag(_Ty) {
 
 template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
 _NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> real(_Ty _Left) {
-    return static_cast<_Upgrade_to_double<_Ty>>(_Left);
+    using _Upgraded = _Upgrade_to_double<_Ty>;
+    const auto _Val = static_cast<_Upgraded>(_Left);
+
+    return _Val;
 }
 
 template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
 _NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> norm(_Ty _Left) {
-    return static_cast<_Upgrade_to_double<_Ty>>(_Left * _Left);
+    using _Upgraded = _Upgrade_to_double<_Ty>;
+    const auto _Val = static_cast<_Upgraded>(_Left);
+
+    return _Val * _Val;
 }
 
 template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
-_NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> conj(_Ty _Left) {
-    return static_cast<_Upgrade_to_double<_Ty>>(_Left);
+_NODISCARD _CONSTEXPR20 complex<_Upgrade_to_double<_Ty>> conj(_Ty _Left) {
+    using _Upgraded = _Upgrade_to_double<_Ty>;
+    const auto _Val = static_cast<_Upgraded>(_Left);
+
+    return complex<_Upgraded>(_Val, -_Upgraded{0});
 }
 
 template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
-_NODISCARD _Upgrade_to_double<_Ty> proj(_Ty _Left) {
-    return static_cast<_Upgrade_to_double<_Ty>>(_Left);
+_NODISCARD complex<_Upgrade_to_double<_Ty>> proj(_Ty _Left) {
+    using _Upgraded = _Upgrade_to_double<_Ty>;
+    const auto _Val = static_cast<_Upgraded>(_Left);
+
+    if (_Ctraits<_Upgraded>::_Isinf(_Val)) {
+        // C11 7.3.9.5/2: "z projects to z except that all complex infinities [...]
+        // project to positive infinity on the real axis."
+        return complex<_Upgraded>(_Ctraits<_Upgraded>::_Infv(), 0);
+    }
+
+    return complex<_Upgraded>(_Val, 0);
 }
 
 // FUNCTION TEMPLATE pow
diff --git a/tests/libcxx/expected_results.txt b/tests/libcxx/expected_results.txt
index b91c3caf449..5cb45fccb9a 100644
--- a/tests/libcxx/expected_results.txt
+++ b/tests/libcxx/expected_results.txt
@@ -597,9 +597,7 @@ std/numerics/complex.number/complex.special/float_long_double_implicit.compile.f
 std/re/re.traits/transform.pass.cpp FAIL
 
 # STL bug: Incorrect return types.
-std/numerics/complex.number/cmplx.over/conj.pass.cpp FAIL
 std/numerics/complex.number/cmplx.over/pow.pass.cpp FAIL
-std/numerics/complex.number/cmplx.over/proj.pass.cpp FAIL
 
 # STL bug: Missing <valarray> assignment operators.
 std/numerics/numarray/template.mask.array/mask.array.assign/mask_array.pass.cpp FAIL
@@ -846,6 +844,10 @@ std/iterators/predef.iterators/insert.iterators/back.insert.iterator/types.pass.
 std/iterators/predef.iterators/insert.iterators/front.insert.iterator/types.pass.cpp SKIPPED
 std/iterators/predef.iterators/insert.iterators/insert.iterator/types.pass.cpp SKIPPED
 
+# Tests emit warning C4244: 'argument': conversion from 'T' to 'const std::complex<double>::_Ty', possible loss of data
+std/numerics/complex.number/cmplx.over/conj.pass.cpp:0 FAIL
+std/numerics/complex.number/cmplx.over/proj.pass.cpp:0 FAIL
+
 
 # *** LIKELY STL BUGS ***
 # Not yet analyzed, likely STL bugs. Assertions and other runtime failures.
diff --git a/tests/libcxx/skipped_tests.txt b/tests/libcxx/skipped_tests.txt
index 9f53e131880..dcba77ec788 100644
--- a/tests/libcxx/skipped_tests.txt
+++ b/tests/libcxx/skipped_tests.txt
@@ -597,9 +597,7 @@ numerics\complex.number\complex.special\float_long_double_implicit.compile.fail.
 re\re.traits\transform.pass.cpp
 
 # STL bug: Incorrect return types.
-numerics\complex.number\cmplx.over\conj.pass.cpp
 numerics\complex.number\cmplx.over\pow.pass.cpp
-numerics\complex.number\cmplx.over\proj.pass.cpp
 
 # STL bug: Missing <valarray> assignment operators.
 numerics\numarray\template.mask.array\mask.array.assign\mask_array.pass.cpp
@@ -846,6 +844,10 @@ iterators\predef.iterators\insert.iterators\back.insert.iterator\types.pass.cpp
 iterators\predef.iterators\insert.iterators\front.insert.iterator\types.pass.cpp
 iterators\predef.iterators\insert.iterators\insert.iterator\types.pass.cpp
 
+# Tests emit warning C4244: 'argument': conversion from 'T' to 'const std::complex<double>::_Ty', possible loss of data
+numerics\complex.number\cmplx.over\conj.pass.cpp
+numerics\complex.number\cmplx.over\proj.pass.cpp
+
 
 # *** LIKELY STL BUGS ***
 # Not yet analyzed, likely STL bugs. Assertions and other runtime failures.
diff --git a/tests/std/tests/Dev10_555491_complex_linker_errors/test.cpp b/tests/std/tests/Dev10_555491_complex_linker_errors/test.cpp
index 781374770d4..77e1fdbd773 100644
--- a/tests/std/tests/Dev10_555491_complex_linker_errors/test.cpp
+++ b/tests/std/tests/Dev10_555491_complex_linker_errors/test.cpp
@@ -2,12 +2,17 @@
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
 #include <assert.h>
+#include <cmath>
 #include <complex>
+#include <limits>
 #include <stdint.h>
 #include <string.h>
+#include <type_traits>
 
 using namespace std;
 
+#define STATIC_ASSERT(...) static_assert(__VA_ARGS__, #__VA_ARGS__)
+
 template <class T, class U>
 T pseudo_bit_cast(const U& source) {
     static_assert(sizeof(T) == sizeof(U), "");
@@ -90,4 +95,57 @@ int main() {
     assert(nearly_equal_partwise(asinh(-1e+307 + 2e+307i), -708.3914896859491 + 1.1071487177940904i));
     assert(nearly_equal_partwise(asinh(-2e+37f + 4e+37if), -87.386663f + 1.1071488if));
     assert(nearly_equal_partwise(asinh(-1e+307L + 2e+307il), -708.3914896859491L + 1.1071487177940904il));
+
+    // Also test GH-785 "<complex>: std::arg does not work for negative real values"
+
+    STATIC_ASSERT(is_same_v<decltype(arg(1729)), double>);
+    STATIC_ASSERT(is_same_v<decltype(imag(1729)), double>);
+    STATIC_ASSERT(is_same_v<decltype(real(1729)), double>);
+    STATIC_ASSERT(is_same_v<decltype(norm(1729)), double>);
+    STATIC_ASSERT(is_same_v<decltype(conj(1729)), complex<double>>);
+    STATIC_ASSERT(is_same_v<decltype(proj(1729)), complex<double>>);
+
+    STATIC_ASSERT(is_same_v<decltype(arg(1729.0f)), float>);
+    STATIC_ASSERT(is_same_v<decltype(imag(1729.0f)), float>);
+    STATIC_ASSERT(is_same_v<decltype(real(1729.0f)), float>);
+    STATIC_ASSERT(is_same_v<decltype(norm(1729.0f)), float>);
+    STATIC_ASSERT(is_same_v<decltype(conj(1729.0f)), complex<float>>);
+    STATIC_ASSERT(is_same_v<decltype(proj(1729.0f)), complex<float>>);
+
+    STATIC_ASSERT(is_same_v<decltype(arg(1729.0)), double>);
+    STATIC_ASSERT(is_same_v<decltype(imag(1729.0)), double>);
+    STATIC_ASSERT(is_same_v<decltype(real(1729.0)), double>);
+    STATIC_ASSERT(is_same_v<decltype(norm(1729.0)), double>);
+    STATIC_ASSERT(is_same_v<decltype(conj(1729.0)), complex<double>>);
+    STATIC_ASSERT(is_same_v<decltype(proj(1729.0)), complex<double>>);
+
+    STATIC_ASSERT(is_same_v<decltype(arg(1729.0L)), long double>);
+    STATIC_ASSERT(is_same_v<decltype(imag(1729.0L)), long double>);
+    STATIC_ASSERT(is_same_v<decltype(real(1729.0L)), long double>);
+    STATIC_ASSERT(is_same_v<decltype(norm(1729.0L)), long double>);
+    STATIC_ASSERT(is_same_v<decltype(conj(1729.0L)), complex<long double>>);
+    STATIC_ASSERT(is_same_v<decltype(proj(1729.0L)), complex<long double>>);
+
+    assert((arg(-1.0) == arg(complex<double>{-1.0, 0.0})));
+    assert((arg(-1) == arg(complex<double>{-1.0, 0.0})));
+
+    assert(imag(1729.0) == 0.0);
+    assert(imag(1729) == 0.0);
+
+    assert(real(1729.0) == 1729.0);
+    assert(real(1729) == 1729.0);
+
+    assert(norm(0x1p63) == 0x1p126);
+    assert(norm(0x8000'0000'0000'0000ULL) == 0x1p126);
+
+    assert((conj(1729.0) == complex<double>{1729.0, -0.0}));
+    assert((conj(1729) == complex<double>{1729.0, -0.0}));
+    assert(signbit(conj(1729.0).imag()));
+    assert(signbit(conj(1729).imag()));
+
+    assert((proj(1729.0) == complex<double>{1729.0, 0.0}));
+    assert((proj(1729) == complex<double>{1729.0, 0.0}));
+    constexpr double inf = numeric_limits<double>::infinity();
+    assert((proj(inf) == complex<double>{inf, 0.0}));
+    assert((proj(-inf) == complex<double>{inf, 0.0}));
 }