diff --git a/ext/AccessorsLinearAlgebraExt.jl b/ext/AccessorsLinearAlgebraExt.jl
index ca47b95..9ab4a23 100644
--- a/ext/AccessorsLinearAlgebraExt.jl
+++ b/ext/AccessorsLinearAlgebraExt.jl
@@ -4,7 +4,10 @@ import Accessors: set, @set
 using LinearAlgebra: norm, normalize, diag, diagind
 
 set(arr, ::typeof(normalize), val) = norm(arr) * val
-set(arr, ::typeof(norm), val)      = map(Base.Fix2(*, val / norm(arr)), arr) # should we check val is positive?
+function set(arr, ::typeof(norm), val)
+    omul = iszero(val) ? one(norm(arr)) : norm(arr)
+    map(Base.Fix2(*, val / omul), arr)
+end
 
 set(A, ::typeof(diag), val) = @set A[diagind(A)] = val
 
diff --git a/src/functionlenses.jl b/src/functionlenses.jl
index 2d3b0d5..fd865b7 100644
--- a/src/functionlenses.jl
+++ b/src/functionlenses.jl
@@ -150,7 +150,10 @@ set(x::AbstractString, f::Base.Fix1{typeof(parse), Type{T}}, y::T) where {T} = s
 set(f, ::typeof(inverse), invf) = setinverse(f, invf)
 
 set(obj, ::typeof(Base.splat(atan)), val) = @set Tuple(obj) = hypot(obj...) .* sincos(val)
-set(obj, ::typeof(Base.splat(hypot)), val) = map(Base.Fix2(*, val / hypot(obj...)), obj)
+function set(obj, ::typeof(Base.splat(hypot)), val)
+    omul = iszero(val) ? one(hypot(obj...)) : hypot(obj...)
+    map(Base.Fix2(*, val / omul), obj)
+end
 
 ################################################################################
 ##### strings
diff --git a/test/test_functionlenses.jl b/test/test_functionlenses.jl
index c9c9947..4500d41 100644
--- a/test/test_functionlenses.jl
+++ b/test/test_functionlenses.jl
@@ -268,7 +268,9 @@ end
     @test @set(abs(-2u"m") = 1u"m") === -1u"m"
     @test @set(abs(x) = 10) ≈ 6 + 8im
     @test @set(angle(x) = π/2) ≈ 5im
+    @test set(0, abs, 0) == 0
     @test set(0, abs, 10) == 10
+    @test set(0+0im, abs, 0) == 0+0im
     @test set(0+0im, abs, 10) == 10
     @test set(0+1e-100im, abs, 10) == 10im
     @test_throws DomainError @set(abs(x) = -10)
@@ -300,7 +302,9 @@ end
     @test set((3, 4), norm, 10) === (6., 8.)
     @test set((a=3, b=4), norm, 10) === (a=6., b=8.)
     test_getset_laws(norm, (3, 4), 10, 12)
+    test_getset_laws(norm, (0, 0), 0, 0)
     test_getset_laws(Base.splat(hypot), (3, 4), 10, 12)
+    test_getset_laws(Base.splat(hypot), (0, 0), 0, 0.)
 
     test_getset_laws(!(@optic _.a), (a=true,), false, true)
     test_getset_laws(!(@optic _[1]), (a=true,), false, true)