diff --git a/stdlib/Random/src/Random.jl b/stdlib/Random/src/Random.jl
index a34603b0487d3..61cca042e2e3e 100644
--- a/stdlib/Random/src/Random.jl
+++ b/stdlib/Random/src/Random.jl
@@ -306,8 +306,8 @@ Pick a random element or array of random elements from the set of values specifi
 * an `AbstractDict` or `AbstractSet` object,
 * a string (considered as a collection of characters), or
 * a type: the set of values to pick from is then equivalent to `typemin(S):typemax(S)` for
-  integers (this is not applicable to [`BigInt`](@ref)), and to ``[0, 1)`` for floating
-  point numbers;
+  integers (this is not applicable to [`BigInt`](@ref)), to ``[0, 1)`` for floating
+  point numbers and to ``[0, 1)+i[0, 1)]`` for complex floating point numbers;
 
 `S` defaults to [`Float64`](@ref).
 
diff --git a/stdlib/Random/src/normal.jl b/stdlib/Random/src/normal.jl
index 1bd8b8ba41152..63fb33df642a3 100644
--- a/stdlib/Random/src/normal.jl
+++ b/stdlib/Random/src/normal.jl
@@ -18,7 +18,7 @@ Optionally generate an array of normally-distributed random numbers.
 The `Base` module currently provides an implementation for the types
 [`Float16`](@ref), [`Float32`](@ref), and [`Float64`](@ref) (the default), and their
 [`Complex`](@ref) counterparts. When the type argument is complex, the values are drawn
-from the circularly symmetric complex normal distribution.
+from the circularly symmetric complex normal distribution of variance 1 (corresponding to real and imaginary part having independent normal distribution with mean zero and variance `1/2`).
 
 # Examples
 ```jldoctest