write the expression in the form a + bi.

$\sqrt{-1} + 9 - \sqrt{-9}$

$\sqrt{-1} + 9 - \sqrt{-9} = $

(simplify your answer. type your answer in the form a + bi. type an exact answer, using radicals as needed.)

Question

write the expression in the form a + bi.

$\sqrt{-1} + 9 - \sqrt{-9}$

$\sqrt{-1} + 9 - \sqrt{-9} = $

(simplify your answer. type your answer in the form a + bi. type an exact answer, using radicals as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Imaginary Unit", "Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Imaginary Unit", "Complex Numbers" ] } ## Simplify the square roots of negative numbers Using the *Imaginary Unit* knowledge point $$ \begin{aligned} &\sqrt{-1} = i\ &\sqrt{-9} = \sqrt{9} \cdot \sqrt{-1} = 3i \end{aligned} $$ ## Substitute and combine like terms Using the *Complex Numbers* knowledge point $$ \begin{aligned} &\sqrt{-1} + 9 - \sqrt{-9} = i + 9 - 3i\ &i + 9 - 3i = 9 + (1 - 3)i = 9 - 2i \end{aligned} $$ Write the expression in the form $a + bi$. $\sqrt{-1} + 9 - \sqrt{-9} =$ $9 - 2i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the square roots of negative numbers

Substitute and combine like terms

Answer: