write the expression in terms of $i$ and simplify.

\\sqrt{-9}\sqrt{-25} = \square\

Question

write the expression in terms of $i$ and simplify.

\\sqrt{-9}\sqrt{-25} = \square\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Imaginary Numbers", "Complex Multiplication" ], "current_concepts": [ "Imaginary Numbers", "Complex Multiplication" ] } ## Express square roots in terms of $i$ $$ \begin{aligned} \sqrt{-9} &= \sqrt{9} \cdot \sqrt{-1} = 3i \ \sqrt{-25} &= \sqrt{25} \cdot \sqrt{-1} = 5i \end{aligned} $$ ## Multiply the imaginary terms $$ (3i)(5i) = 15i^2 $$ ## Simplify using $i^2 = -1$ $$ 15i^2 = 15(-1) = -15 $$ Write the expression in terms of $i$ and simplify. $\sqrt{-9}\sqrt{-25} =$ -15 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Imaginary Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Express square roots in terms of \(i\)

Multiply the imaginary terms

Simplify using \(i^2 = -1\)

Answer: