Consider computing the product of two complex numbers (a + bi) and (c + di). By foiling the polynomials as we learned in grade school. We get:

a + bi

c + di

----------

adi - bd

ca + cbi

----------------

(ca - bd) + (ad + cb)i

Note that this standard method uses 4 multiplications and 2 additions to compute the product. (The plus sign in between (ca - bd) and (ad + cb)i does not count as an addition. Think of a complex number as simply a 2-tuple.)

It is actually possible to compute this complex product using only 3 multiplications and 3 additions. From a logic design perspective, this is preferable since multiplications are more expensive to implement than additions. Can you figure out how to do this?

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