Question

select the correct answer.

which of the following is a non-real complex number?

\\(9 - \frac{1}{\sqrt{17}}\\)

\\(3\sqrt{\frac{7}{5}} + \sqrt{-\frac{9}{5}}\\)

\\(\frac{5 - 2\sqrt{7}}{4}\\)

\\(-8\sqrt{\frac{1}{6}} - \frac{3}{\sqrt{2}}\\)

Explanation:

Define non-real complex numbers

$$ z = a + bi \quad (a, b \in \mathbb{R}) \text{ is non-real if } b eq 0 \text{, which requires a negative radicand under an even root.} $$

Analyze each option

$$
LATEXBLOCK0
$$

Identify the correct option

$$ 3\sqrt{\frac{7}{5}} + \sqrt{-\frac{9}{5}} \text{ contains } \sqrt{-\frac{9}{5}} \text{, which is an imaginary number.} $$

Answer:

• (A) \(9 - \frac{1}{\sqrt{17}}\)
• (B) \(3\sqrt{\frac{7}{5}} + \sqrt{-\frac{9}{5}}\) (Correct answer)
• (C) \(\frac{5 - 2\sqrt{7}}{4}\)
• (D) \(-8\sqrt{\frac{1}{6}} - \frac{3}{\sqrt{2}}\)