diff --git a/src/Utilities/distance_to_set.jl b/src/Utilities/distance_to_set.jl
index 83e76ef51a..7039d818cb 100644
--- a/src/Utilities/distance_to_set.jl
+++ b/src/Utilities/distance_to_set.jl
@@ -194,7 +194,7 @@ function _reshape(
         MOI.LogDetConeTriangle,
         MOI.RootDetConeTriangle,
     },
-) where {T}
+) where {T<:Real}
     n = isqrt(2 * length(x))
     # The type annotation is needed for JET.
     X = zeros(T, n, n)::Matrix{T}
@@ -208,6 +208,24 @@ function _reshape(
     return LinearAlgebra.Symmetric(X)
 end
 
+function _reshape(
+    x::AbstractVector{T},
+    set::MOI.PositiveSemidefiniteConeTriangle,
+) where {T<:Complex}
+    n = isqrt(2 * length(x))
+    # The type annotation is needed for JET.
+    X = zeros(T, n, n)::Matrix{T}
+    k = 1
+    for i in 1:n
+        for j in 1:i
+            X[i, j] = conj(x[k])
+            X[j, i] = x[k]
+            k += 1
+        end
+    end
+    return LinearAlgebra.Hermitian(X)
+end
+
 # This is the minimal L2-norm.
 function distance_to_set(
     ::ProjectionUpperBoundDistance,
@@ -553,7 +571,7 @@ function distance_to_set(
         MOI.PositiveSemidefiniteConeSquare,
         MOI.PositiveSemidefiniteConeTriangle,
     },
-) where {T<:Real}
+) where {T<:Union{Real,Complex}}
     _check_dimension(x, set)
     # We should return the norm of `A` defined by:
     # ```julia
@@ -565,8 +583,7 @@ function distance_to_set(
     # The norm should correspond to `MOI.Utilities.set_dot` so it's the
     # Frobenius norm, which is the Euclidean norm of the vector of eigenvalues.
     eigvals = LinearAlgebra.eigvals(_reshape(x, set))
-    eigvals .= min.(zero(T), eigvals)
-    return LinearAlgebra.norm(eigvals, 2)
+    return LinearAlgebra.norm(min.(0, eigvals), 2)
 end
 
 """
@@ -702,3 +719,44 @@ function distance_to_set(
     push!(eigvals_neg, max(x[1] - x[2] * sum(log.(eigvals_pos)), zero(T)))
     return LinearAlgebra.norm(eigvals_neg, 2)
 end
+
+"""
+    distance_to_set(
+        ::ProjectionUpperBoundDistance,
+        x::AbstractVector,
+        set::MOI.Scaled{S},
+    )
+
+This is the distance in the un-scaled space.
+"""
+function distance_to_set(
+    dist::ProjectionUpperBoundDistance,
+    x::AbstractVector{T},
+    set::MOI.Scaled{S},
+) where {T,S<:MOI.AbstractVectorSet}
+    _check_dimension(x, set)
+    scale = MOI.Utilities.SetDotScalingVector{T}(set.set)
+    return distance_to_set(dist, x ./ scale, set.set)
+end
+
+function distance_to_set(
+    dist::ProjectionUpperBoundDistance,
+    x::AbstractVector{T},
+    set::MOI.HermitianPositiveSemidefiniteConeTriangle,
+) where {T<:Real}
+    _check_dimension(x, set)
+    output_set = MOI.PositiveSemidefiniteConeTriangle(set.side_dimension)
+    y = zeros(Complex{T}, MOI.dimension(output_set))
+    real_offset, imag_offset = 0, length(y)
+    for col in 1:set.side_dimension
+        for row in 1:col
+            real_offset += 1
+            y[real_offset] = x[real_offset]
+            if row != col
+                imag_offset += 1
+                y[real_offset] += x[imag_offset] * im
+            end
+        end
+    end
+    return distance_to_set(dist, y, output_set)
+end
diff --git a/test/Utilities/distance_to_set.jl b/test/Utilities/distance_to_set.jl
index 6016d09421..49739e90b7 100644
--- a/test/Utilities/distance_to_set.jl
+++ b/test/Utilities/distance_to_set.jl
@@ -320,7 +320,8 @@ function test_positivesemidefiniteconesquare()
         [1.0, 0.0, 0.0, 1.0] => 0.0,
         [1.0, -1.0, -1.0, 1.0] => 0.0,
         [1.0, -2.0, -2.0, 1.0] => 1.0,
-        [1.0, 1.1, 1.1, -2.3] => 2.633053201505194;
+        [1.0, 1.1, 1.1, -2.3] => 2.633053201505194,
+        [1.0, -2.0, -2.0, 1.0] => 1.0;
         mismatch = [1.0],
     )
     return
@@ -476,6 +477,44 @@ function test_LogDetConeSquare()
     return
 end
 
+function test_Scaled()
+    _test_set(
+        MOI.Scaled(MOI.PositiveSemidefiniteConeTriangle(2)),
+        [1.0, 0.0, 1.0] => 0.0,
+        [1.0, -1.0, 1.0] => 0.0,
+        [1.0, -2.0 * sqrt(2), 1.0] => 1.0,
+        [1.0, 1.1 * sqrt(2), -2.3] => 2.633053201505194;
+        mismatch = [1.0],
+    )
+    return
+end
+
+function test_PositiveSemidefiniteConeTriangle_Complex()
+    _test_set(
+        MOI.PositiveSemidefiniteConeTriangle(2),
+        ComplexF64[1.0, 0.0, 1.0] => 0.0,
+        ComplexF64[1.0, -1.0, 1.0] => 0.0,
+        ComplexF64[1.0, -2.0, 1.0] => 1.0,
+        ComplexF64[1.0, 1.1, -2.3] => 2.633053201505194,
+        ComplexF64[1.0, 1-im, 1.0] => 0.41421356237309537;
+        mismatch = [1.0],
+    )
+    return
+end
+
+function test_HermitianPositiveSemidefiniteConeTriangle()
+    _test_set(
+        MOI.HermitianPositiveSemidefiniteConeTriangle(2),
+        [1.0, 0.0, 1.0, 0.0] => 0.0,
+        [1.0, -1.0, 1.0, 0.0] => 0.0,
+        [1.0, -2.0, 1.0, 0.0] => 1.0,
+        [1.0, 1.1, -2.3, 0.0] => 2.633053201505194,
+        [1.0, 1.0, 1.0, -1.0] => 0.41421356237309537;
+        mismatch = [1.0],
+    )
+    return
+end
+
 end
 
 TestFeasibilityChecker.runtests()