perform all operations. give your answer in $a + bi$ form.
\(4 - 5i)^2\

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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 Multiplication" ], "new_concepts": [], "current_concepts": [ "Complex Number Multiplication", "Imaginary Numbers" ] } ## Expand the squared binomial $$ (4 - 5i)^2 = 4^2 - 2(4)(5i) + (5i)^2 $$ ## Simplify the terms $$ \begin{aligned} 4^2 &= 16 \ -2(4)(5i) &= -40i \ (5i)^2 &= 25i^2 \end{aligned} $$ ## Substitute $i^2 = -1$ and combine real parts $$ \begin{aligned} 16 - 40i + 25(-1) &= 16 - 40i - 25 \ &= -9 - 40i \end{aligned} $$ Perform all operations. Give your answer in $a + bi$ form. $$(4 - 5i)^2$$ $-9 - 40i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Number Multiplication" ] }

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Question

Explanation:

Expand the squared binomial

Simplify the terms

Substitute \(i^2 = -1\) and combine real parts

Answer: