Let x 1 (t) and x 2 (t) be two real-valued signals. Show that the square of

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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).

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