perform all operations. give the answer in $a + bi$ form.

\(8 + \sqrt{-9}) - (26i - 34)\

Question

perform all operations. give the answer in $a + bi$ form.

\(8 + \sqrt{-9}) - (26i - 34)\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Imaginary Numbers", "Complex Number Subtraction" ], "new_concepts": [], "current_concepts": [ "Imaginary Numbers", "Complex Number Subtraction" ] } ## Simplify the radical term $$ \sqrt{-9} = \sqrt{9} \cdot \sqrt{-1} = 3i $$ ## Rewrite the expression $$ (8 + 3i) - (26i - 34) $$ ## Distribute and combine like terms $$ \begin{aligned} (8 + 3i) - 26i + 34 &= (8 + 34) + (3i - 26i) \ &= 42 - 23i \end{aligned} $$ Perform all operations. Give the answer in $a + bi$ form. $$(8 + \sqrt{-9}) - (26i - 34)$$ $42 - 23i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

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Question

Explanation:

Simplify the radical term

Rewrite the expression

Distribute and combine like terms

Answer: