\\frac{6 + \sqrt{-81}}{3} =\

\\frac{25 + \sqrt{-64}}{9} =\

Question

\\frac{6 + \sqrt{-81}}{3} =\

\\frac{25 + \sqrt{-64}}{9} =\

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Imaginary Unit", "Complex Numbers", "Simplifying Radicals", "Complex Number Division" ], "new_concepts": [], "current_concepts": [ "Imaginary Unit", "Complex Numbers", "Simplifying Radicals", "Complex Number Division" ] } ## Simplify the radical terms Using the *Imaginary Unit* and *Simplifying Radicals* knowledge points $$ \begin{aligned} \sqrt{-81} &= \sqrt{81} \cdot \sqrt{-1} = 9i \ \sqrt{-64} &= \sqrt{64} \cdot \sqrt{-1} = 8i \end{aligned} $$ ## Substitute and divide the first expression Using the *Complex Number Division* and *Complex Numbers* knowledge points $$ \begin{aligned} \frac{6 + \sqrt{-81}}{3} &= \frac{6 + 9i}{3} \ &= \frac{6}{3} + \frac{9i}{3} \ &= 2 + 3i \end{aligned} $$ ## Substitute and divide the second expression Using the *Complex Number Division* and *Complex Numbers* knowledge points $$ \begin{aligned} \frac{25 + \sqrt{-64}}{9} &= \frac{25 + 8i}{9} \ &= \frac{25}{9} + \frac{8}{9}i \end{aligned} $$ ## Question 1 $2 + 3i$ ## Question 2 $\frac{25}{9} + \frac{8}{9}i$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the radical terms

Substitute and divide the first expression

Substitute and divide the second expression

Answer:

Question 1

Question 2