diff --git a/library/core/src/num/complex.rs b/library/core/src/num/complex.rs
index 66126c52fadad..c6a56285cdfb1 100644
--- a/library/core/src/num/complex.rs
+++ b/library/core/src/num/complex.rs
@@ -1,4 +1,5 @@
-use crate::ops::{Add, Neg, Sub};
+use crate::num::imp::libm::complex::*;
+use crate::ops::{Add, Div, Mul, Neg, Sub};
 
 /// A complex number.
 #[derive(Clone, Copy, Debug, PartialEq, Eq)]
@@ -91,3 +92,54 @@ impl<T: Sub<Output = T>> Sub<T> for Complex<T> {
         Complex::new(self.re - rhs, self.im)
     }
 }
+
+macro_rules! impl_complex_mul_div {
+    ($ty:ty, $mul:ident, $div:ident) => {
+        #[unstable(feature = "complex_numbers", issue = "154023")]
+        impl Mul for Complex<$ty> {
+            type Output = Self;
+
+            #[inline]
+            fn mul(self, rhs: Self) -> Self::Output {
+                let Complex { re: a, im: b } = self;
+                let Complex { re: c, im: d } = rhs;
+
+                let ac = a * c;
+                let bd = b * d;
+                let ad = a * d;
+                let bc = b * c;
+
+                let z = Complex::new(ac - bd, ad + bc);
+
+                // Only call the libcall when both components are NaN.
+                //
+                // The naive algorithm would return NaN + NaNi for an input like
+                // (1 + 0i) * (inf + infi). The libcall instead returns inf + infi.
+                //
+                // We duplicate the fast path here so that it can be inlined. We use a libcall
+                // for the NaN correction to reduce the size of `core`.
+                if z.re.is_nan() && z.im.is_nan() {
+                    crate::hint::cold_path();
+                    $mul(a, b, c, d)
+                } else {
+                    z
+                }
+            }
+        }
+
+        #[unstable(feature = "complex_numbers", issue = "154023")]
+        impl Div for Complex<$ty> {
+            type Output = Self;
+
+            #[inline]
+            fn div(self, rhs: Self) -> Self::Output {
+                $div(self.re, self.im, rhs.re, rhs.im)
+            }
+        }
+    };
+}
+
+impl_complex_mul_div!(f16, __rust_mulhc3, __rust_divhc3);
+impl_complex_mul_div!(f32, __mulsc3, __divsc3);
+impl_complex_mul_div!(f64, __muldc3, __divdc3);
+impl_complex_mul_div!(f128, __rust_multc3, __rust_divtc3);
diff --git a/library/core/src/num/imp/libm.rs b/library/core/src/num/imp/libm.rs
index 388f1479b2461..8e035dc516260 100644
--- a/library/core/src/num/imp/libm.rs
+++ b/library/core/src/num/imp/libm.rs
@@ -75,6 +75,27 @@ unsafe extern "C" {
     pub(crate) safe fn truncf16(x: f16) -> f16;
 }
 
+/// These symbols are always provided by compiler-builtins.
+pub(crate) mod complex {
+    use crate::num::Complex;
+
+    unsafe extern "C" {
+        pub(crate) safe fn __mulsc3(a: f32, b: f32, c: f32, d: f32) -> Complex<f32>;
+        pub(crate) safe fn __muldc3(a: f64, b: f64, c: f64, d: f64) -> Complex<f64>;
+
+        pub(crate) safe fn __divsc3(a: f32, b: f32, c: f32, d: f32) -> Complex<f32>;
+        pub(crate) safe fn __divdc3(a: f64, b: f64, c: f64, d: f64) -> Complex<f64>;
+    }
+
+    unsafe extern "Rust" {
+        pub(crate) safe fn __rust_mulhc3(a: f16, b: f16, c: f16, d: f16) -> Complex<f16>;
+        pub(crate) safe fn __rust_multc3(a: f128, b: f128, c: f128, d: f128) -> Complex<f128>;
+
+        pub(crate) safe fn __rust_divhc3(a: f16, b: f16, c: f16, d: f16) -> Complex<f16>;
+        pub(crate) safe fn __rust_divtc3(a: f128, b: f128, c: f128, d: f128) -> Complex<f128>;
+    }
+}
+
 /// These symbols will be available when `std` is available, and on many no-std platforms. However,
 /// since this isn't a guarantee, we cannot rely on them for stable implementations.
 pub(crate) mod likely_available {
diff --git a/library/coretests/tests/num/complex.rs b/library/coretests/tests/num/complex.rs
index c22c5b9575b3d..ea7bff0acc7de 100644
--- a/library/coretests/tests/num/complex.rs
+++ b/library/coretests/tests/num/complex.rs
@@ -73,3 +73,63 @@ fn complex_negation() {
     assert_eq!(-Complex::new(1.0, -2.0), Complex::new(-1.0, 2.0));
     assert_eq!(-Complex::new(1.0, f32::INFINITY), Complex::new(-1.0, f32::NEG_INFINITY),);
 }
+
+#[test]
+fn complex_multiplication() {
+    #[cfg(target_has_reliable_f16)]
+    assert_eq!(Complex::new(1.0f16, 2.0) * Complex::new(3.0, 4.0), Complex::new(-5.0, 10.0));
+    assert_eq!(Complex::new(1.0f32, 2.0) * Complex::new(3.0, 4.0), Complex::new(-5.0, 10.0));
+    assert_eq!(Complex::new(1.0f64, 2.0) * Complex::new(3.0, 4.0), Complex::new(-5.0, 10.0));
+    #[cfg(target_has_reliable_f128)]
+    assert_eq!(Complex::new(1.0f128, 2.0) * Complex::new(3.0, 4.0), Complex::new(-5.0, 10.0));
+
+    // The naive algorithm would return NaN + NaNi for these inputs, but the libcall handles it.
+    #[cfg(target_has_reliable_f16)]
+    assert_eq!(
+        Complex::new(1.0, 0.0) * Complex::new(f16::INFINITY, f16::INFINITY),
+        Complex::new(f16::INFINITY, f16::INFINITY)
+    );
+    assert_eq!(
+        Complex::new(1.0, 0.0) * Complex::new(f32::INFINITY, f32::INFINITY),
+        Complex::new(f32::INFINITY, f32::INFINITY)
+    );
+    assert_eq!(
+        Complex::new(1.0, 0.0) * Complex::new(f64::INFINITY, f64::INFINITY),
+        Complex::new(f64::INFINITY, f64::INFINITY)
+    );
+    #[cfg(target_has_reliable_f128)]
+    assert_eq!(
+        Complex::new(1.0, 0.0) * Complex::new(f128::INFINITY, f128::INFINITY),
+        Complex::new(f128::INFINITY, f128::INFINITY)
+    );
+}
+
+#[test]
+fn div() {
+    #[cfg(target_has_reliable_f16)]
+    assert_eq!(Complex::new(2.0f16, 11.0) / Complex::new(2.0, 1.0), Complex::new(3.0, 4.0));
+    assert_eq!(Complex::new(2.0f32, 11.0) / Complex::new(2.0, 1.0), Complex::new(3.0, 4.0));
+    assert_eq!(Complex::new(2.0f64, 11.0) / Complex::new(2.0, 1.0), Complex::new(3.0, 4.0));
+    #[cfg(target_has_reliable_f128)]
+    assert_eq!(Complex::new(2.0f128, 11.0) / Complex::new(2.0, 1.0), Complex::new(3.0, 4.0));
+
+    // The naive algorithm would return NaN + NaNi for these inputs, but the libcall handles it.
+    #[cfg(target_has_reliable_f16)]
+    assert_eq!(
+        Complex::new(f16::INFINITY, 0.0) / Complex::new(1.0, 1.0),
+        Complex::new(f16::INFINITY, f16::NEG_INFINITY)
+    );
+    assert_eq!(
+        Complex::new(f32::INFINITY, 0.0) / Complex::new(1.0, 1.0),
+        Complex::new(f32::INFINITY, f32::NEG_INFINITY)
+    );
+    assert_eq!(
+        Complex::new(f64::INFINITY, 0.0) / Complex::new(1.0, 1.0),
+        Complex::new(f64::INFINITY, f64::NEG_INFINITY)
+    );
+    #[cfg(target_has_reliable_f128)]
+    assert_eq!(
+        Complex::new(f128::INFINITY, 0.0) / Complex::new(1.0, 1.0),
+        Complex::new(f128::INFINITY, f128::NEG_INFINITY)
+    );
+}