type the correct answer in each box.

what values of $a$ and $b$ make this equation true?

$4 + \sqrt{-49}) - 2(\sqrt{(-4)^2} + \sqrt{-324}) = a + bi\

\(a = $
$b = $

Question

type the correct answer in each box.

what values of $a$ and $b$ make this equation true?

$4 + \sqrt{-49}) - 2(\sqrt{(-4)^2} + \sqrt{-324}) = a + bi\

\(a = $
$b = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Number Arithmetic", "Real and Imaginary Numbers", "Equality of Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Complex Number Arithmetic", "Real and Imaginary Numbers", "Equality of Complex Numbers" ] } ## Simplify the radical terms $$ \begin{aligned} \sqrt{-49} &= 7i \ \sqrt{(-4)^2} &= \sqrt{16} = 4 \ \sqrt{-324} &= 18i \end{aligned} $$ ## Substitute and expand the expression $$ \begin{aligned} (4 + 7i) - 2(4 + 18i) &= 4 + 7i - 8 - 36i \ &= (4 - 8) + (7i - 36i) \ &= -4 - 29i \end{aligned} $$ ## Equate to find a and b $$ \begin{aligned} a + bi &= -4 - 29i \ a &= -4 \ b &= -29 \end{aligned} $$ What values of $a$ and $b$ make this equation true? $$(4 + \sqrt{-49}) - 2(\sqrt{(-4)^2} + \sqrt{-324}) = a + bi$$ $a =$ -4 $b =$ -29 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Number Arithmetic" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the radical terms

Substitute and expand the expression

Equate to find a and b

Answer: