question 4
part a

enter the correct answer in the box.

rewrite the expression $\frac{4 + \sqrt{16 - (4)(5)}}{2}$ as a complex number in standard form, $a + bi$.

Question

question 4
part a

enter the correct answer in the box.

rewrite the expression $\frac{4 + \sqrt{16 - (4)(5)}}{2}$ as a complex number in standard 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": [ "Complex Numbers", "Simplifying Radicals with Negative Radicands" ], "new_concepts": [], "current_concepts": [ "Complex Numbers", "Simplifying Radicals with Negative Radicands" ] } ## Simplify the radical term $$ \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i $$ ## Substitute and simplify the expression $$ \begin{aligned} \frac{4 + \sqrt{-16}}{2} - (4)(5) &= \frac{4 + 4i}{2} - 20 \ &= (2 + 2i) - 20 \end{aligned} $$ ## Write in standard form $a + bi$ $$ (2 - 20) + 2i = -18 + 2i $$ Rewrite the expression $\frac{4 + \sqrt{-16}}{2} - (4)(5)$ as a complex number in standard form, $a + bi$. $-18 + 2i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

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Question

Explanation:

Simplify the radical term

Substitute and simplify the expression

Write in standard form \(a + bi\)

Answer: