SOLUTION: Which of the following statments are always true?
(1) The sum of two imaginary numbers is an imaginary number
(2) A real number is a complex number
(3) A complex number is an im
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Question 232818: Which of the following statments are always true?
(1) The sum of two imaginary numbers is an imaginary number
(2) A real number is a complex number
(3) A complex number is an imaginary number
(4) The product of two imaginary numbers is a real number
--------------------------------------------------------------------------------Please answer the question and explain how to get the answer :) Thank you
Found 2 solutions by rapaljer, Alan3354:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
2) Every real number is a complex number is a true statement. Each real number can be expressed as a complex number a+bi where b=0. The other statements are not always true.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Which of the following statments are always true?
(1) The sum of two imaginary numbers is an imaginary number
This is true unless the sum is zero.
2i + 3i = 5i
ai + bi = (a+b)i
4i + (-4i) = 0
Always an i unless a = -b, then it's zero (0).
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(2) A real number is a complex number
Any real number can be presented as a complex number.
4 = 4 + 0i = 4 - 0i
The definition of "complex number" determines where 0i is included.
Chances are False is the answer expected, tho.
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(3) A complex number is an imaginary number
A complex number is a real part + imaginary part. Like the one above, tho, it can be 0 + 3i, or 0 - bi.
I think False is expected.
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(4) The product of two imaginary numbers is a real number
True. ai x bi = -ab
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