Computing the DFT generally requires complex multiplications. Consider the product X + jY = (A + jB)(C + jD) = (AC − BD) + j (BC + AD). In this form, a complex multiplication requires four real multiplications and two real additions. Verify that a complex multiplication can be performed with three real multiplications and five additions using the algorithm
X = (A − B)D + (C − D)A,
Y = (A − B)D + (C + D)B.
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