diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index f6e1475b00ecfbb..edd369313084d73 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -477,6 +477,9 @@ cmath_cosh_impl(PyObject *module, Py_complex z)
         x_minus_one = z.real - copysign(1., z.real);
         r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
         r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
+        if (isnan(r.imag)) {
+            r.imag = copysign(0., z.real*z.imag);
+        }
     } else {
         r.real = cos(z.imag) * cosh(z.real);
         r.imag = sin(z.imag) * sinh(z.real);
@@ -737,6 +740,9 @@ cmath_sinh_impl(PyObject *module, Py_complex z)
         x_minus_one = z.real - copysign(1., z.real);
         r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
         r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
+        if (isnan(r.imag)) {
+            r.imag = copysign(0., z.imag);
+        }
     } else {
         r.real = cos(z.imag) * sinh(z.real);
         r.imag = sin(z.imag) * cosh(z.real);