✔ 最佳答案
Q1.A. The sum of two irrational numbers can be rational.
True. For example , √2 + (3 - √2) = 3.
B. The product of two irratoinal numbers can be rational.
True. For example , √2 * √8 = 4.
C.The product of non-zero rational number and irrational number can be rational.False.
Let R be the rational number , I be the irrational number.
Assuming that R * I = P is rational , then
I = P / R is rational since P , R are rational. (Contradiction)
D. The product of two rational numbers must be rational. True.
Let m/n and p/q be two rational numbers ,
were m , n , p , q are integers , then the product
= m/n * p/q = mp / (nq) must be rational.
∴ C. must NOT be correct.
Choose C.
Q2.I. 8 is not a complex number.False.
8 is a complex number with the form 8 + 0i .
II. - i = 1/iTrue.
- i = - i * i / i = - (i²) / i = - (-1) / i = 1 / i
III. 2i - 5 = i(2+5i)True.
i(2+5i) = 2i + 5i² = 2i + 5(-1) = 2i - 5
∴ II and III are correct , I must not correct.
Choose C. II and III only.
