Question 233417
 If a and b are real numbers, then the product of a+bi and a-bi is
(1) always imaginary
(2) always a real number
(3) sometimes,but not always, a real number
(4) sometimes,but not always, imaginary
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(a+bi)(a-bi) = a^2 +abi -abi -(bi)^2
= a^2 + b^2
and this is always a Real Number because 
a and b are always Real Numbers.
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Cheers,
Stan H.