SOLUTION: 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 no

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 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 no      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

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
----------------------------------------------------------------------------------
Please help choose the correct answer choice and please explain how to get the answer Thank you
Answer by stanbon(26297) About Me  (Show Source):
You can put this solution on YOUR website!
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
----------------
(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.
=========================================
Cheers,
Stan H.