Let x₁(t) and x₂(t) be two real-valued signals. Show that the square of the norm of the signal x₁(t) + x₂(t) is the sum of the square of the norm of x₁(t) and the square of the norm of x₂(t), if and only if x₁(t) and x₂(t) are orthogonal; that is, ||x₁ + x₂||² = ||x₁||² + ||x₂||² if and only if (x₁, x₂) = 0. Note the analogy to vectors in three dimensional space: the Pythagorean theorem applies only to vectors that are orthogonal or perpendicular (zero dot product).