Question 232815: 1. 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) Somtimes, but not always, a real number
(4) Somtimes, but not alwaus, imaginary
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Please help me with this question and explain how you got the answer thank you
Found 3 solutions by rapaljer, Alan3354, jsmallt9:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Always real!
(a+bi)(a-bi)
a^2 -abi + abi - b^2 i^2
a^2 -b^2 *-1
a^2 + b^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Answer by Alan3354(69443)  (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
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It's 2, always a real number.
Multiply them.
(a+bi)*(a-bi) = a^2 - (bi)^2
= a^2 - (-b^2)
= a^2 + b^2
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example:
(2+3i)*(2-3i) = 4+9 = 13
Answer by jsmallt9(3758)  (Show Source):
You can put this solution on YOUR website! Let's multiply a+bi and a-bi and see what happens:
The i's have disappeared. We're told that a and b are real numbers. Then  is also a real number. Your answer is (2).
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