Think hard?
The sum of two irrational numbers is always irrational.
The sum of two rational numbers is always rational.
The sum of two complex numbers is always complex.
Of the 3 statements given above, how many of these statements are true?
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1 solution
The first is wrong, consider ( 1 + 2 ) + ( − 2 ) = 1
The second is correct.
( a , c ∈ Z , b , d ∈ N ) , b a + d c = b d a d + b c ∈ Q
The third is correct.
( a , b , c , d ∈ R ) , ( a + b i ) + ( c + d i ) = ( a + c ) + ( b + d ) i ∈ C
Note that the difference between the first statement and the third statement is that even a pure real number (imaginary part = 0) is a complex number.