Question

select the correct answer.

one solution to a quadratic function, \\(g\\), is given.

\\9 - \sqrt{2}i\\

which statement is true?

• function \\(g\\) has no other solutions.
• the other solution to function \\(g\\) is \\(-9 + \sqrt{2}i\\).
• the other solution to function \\(g\\) is \\(-9 - \sqrt{2}i\\).
• the other solution to function \\(g\\) is \\(9 + \sqrt{2}i\\).

Explanation:

Identify the given complex solution

$$ z_1 = 9 - \sqrt{2}i $$

Apply the Complex Conjugate Root Theorem

$$
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Match with the correct option

$$ \text{The other solution to function } g \text{ is } 9 + \sqrt{2}i. $$

Answer:

• Function \(g\) has no other solutions.
• The other solution to function \(g\) is \(-9 + \sqrt{2}i\).
• The other solution to function \(g\) is \(-9 - \sqrt{2}i\).
• The other solution to function \(g\) is \(9 + \sqrt{2}i\). (Correct answer)