Question 232818
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