multiply.

$(4 + \sqrt{-9})(2 + \sqrt{-25})$

$(4 + \sqrt{-9})(2 + \sqrt{-25}) = $

(simplify your answer. type your answer in the form $a + bi$.)

Question

multiply.

$(4 + \sqrt{-9})(2 + \sqrt{-25})$

$(4 + \sqrt{-9})(2 + \sqrt{-25}) = $

(simplify your answer. type your answer in the form $a + bi$.)

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", "Simplifying Radicals", "Complex Number Multiplication" ], "new_concepts": [], "current_concepts": [ "Imaginary Numbers", "Simplifying Radicals", "Complex Number Multiplication" ] } ## Simplify the radicals $$ \begin{aligned} \sqrt{-9} &= 3i \ \sqrt{-25} &= 5i \end{aligned} $$ ## Rewrite the expression $$ (4 + 3i)(2 + 5i) $$ ## Multiply the complex numbers $$ \begin{aligned} (4 + 3i)(2 + 5i) &= 4(2) + 4(5i) + 3i(2) + 3i(5i) \ &= 8 + 20i + 6i + 15i^2 \ &= 8 + 26i + 15(-1) \ &= 8 - 15 + 26i \ &= -7 + 26i \end{aligned} $$ $(4 + \sqrt{-9})(2 + \sqrt{-25}) =$ $-7 + 26i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Number Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the radicals

Rewrite the expression

Multiply the complex numbers

Answer: