SOLUTION: 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, bu

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(4551)   (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(21588)   (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(2063)   (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).