diff --git a/src/complex_float.rs b/src/complex_float.rs
index 873fe73..5b1c143 100644
--- a/src/complex_float.rs
+++ b/src/complex_float.rs
@@ -144,6 +144,22 @@ pub trait ComplexFloat: Num + NumCast + Copy + Neg<Output = Self> + private::Sea
     ///
     /// Formula: `a+bi -> a-bi`
     fn conj(self) -> Self;
+
+    /// Returns ln(1+n) (natural logarithm) more accurately
+    /// than if the operations were performed separately
+    ///
+    /// Formula: ln(1+z)
+    ///
+    /// where z = a+bi
+    fn ln_1p(self) -> Self;
+
+    /// Returns e^(self) - 1 in a way that is accurate
+    /// even if the number is close to zero
+    ///
+    /// Formaula: e^(z) - 1
+    ///
+    /// where z = a+bi
+    fn exp_m1(self) -> Self;
 }
 
 macro_rules! forward {
@@ -235,6 +251,8 @@ where
         Float::acosh(self) -> Self;
         Float::atanh(self) -> Self;
         Float::abs(self) -> Self;
+        Float::ln_1p(self) -> Self;
+        Float::exp_m1(self) -> Self;
     }
 }
 
@@ -306,6 +324,8 @@ impl<T: Float + FloatConst> ComplexFloat for Complex<T> {
         Complex::asinh(self) -> Self;
         Complex::acosh(self) -> Self;
         Complex::atanh(self) -> Self;
+        Complex::ln_1p(self) -> Self;
+        Complex::exp_m1(self) -> Self;
     }
 
     forward_ref! {
diff --git a/src/lib.rs b/src/lib.rs
index 661b67b..3e3732c 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -624,6 +624,48 @@ impl<T: Float> Complex<T> {
     pub fn fdiv(self, other: Complex<T>) -> Complex<T> {
         self * other.finv()
     }
+
+    /// The ln_1p() function computes the natural logarithm
+    /// of (1 + z), which is particularly useful for
+    /// small values of `z` to avoid loss of precision
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// use num_complex::Complex64;
+    /// use num_complex::ComplexFloat;
+    ///
+    /// let a = Complex64::new(2.0e-16, 3.0e-16);
+    ///
+    /// let approx_val = a.ln_1p();
+    /// let expected_val = Complex64::new(2.2204e-16, 2.999e-16);
+    /// assert!((approx_val - expected_val).norm() < 1e-18);
+    /// ```
+    #[inline]
+    pub fn ln_1p(self) -> Self {
+        (Self::one() + self).ln()
+    }
+
+    /// The exp_m1() function computes the exponential
+    /// of z minus one (`e^(z) - 1`), which is particularly
+    /// useful for small values of `z` to avoid loss of precision
+    ///
+    /// # Examples
+    ///
+    /// ```rust
+    /// use num_complex::Complex64;
+    /// use num_complex::ComplexFloat;
+    ///
+    /// let a = Complex64::new(2.0e-16, 3.0e-16);
+    ///
+    /// let approx_val = a.exp_m1();
+    /// let expected_val = Complex64::new(2.2204e-16, 3.0e-16);
+    /// assert!((approx_val - expected_val).norm() < 1e-18);
+    /// ```
+    #[inline]
+    pub fn exp_m1(self) -> Self {
+        self.exp() - Self::one()
+    }
 }
 
 #[cfg(any(feature = "std", feature = "libm"))]
@@ -2432,6 +2474,22 @@ pub(crate) mod test {
                 ));
             }
         }
+
+        #[test]
+        fn test_ln_1p() {
+            for &c in all_consts.iter() {
+                // ln_1p(z) = ln(1+z)
+                assert!(close(c.ln_1p(), (1.0 + c).ln()));
+            }
+        }
+
+        #[test]
+        fn test_exp_m1() {
+            for &c in all_consts.iter() {
+                // exp_m1(z) = exp(z) - 1
+                assert!(close(c.exp_m1(), (c).exp() - 1.0));
+            }
+        }
     }
 
     // Test both a + b and a += b