type the correct answer in each box.

what are the values of $x$ and $y$ that make the equations true?

| equation a | $(x + yi) + (4 - 7i) = 3 - 4i$ |
|---|---|
| equation b | $(x + yi) - (-6 + 14i) = 18 + 2i$ |

in equation a, $x =$ and $y =$ .
in equation b, $x =$ and $y =$ .

Question

type the correct answer in each box.

what are the values of $x$ and $y$ that make the equations true?

| equation a | $(x + yi) + (4 - 7i) = 3 - 4i$ |
|---|---|
| equation b | $(x + yi) - (-6 + 14i) = 18 + 2i$ |

in equation a, $x =$   and $y =$  .
in equation b, $x =$   and $y =$  .

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Number Arithmetic" ], "new_concepts": [ "Equality of Complex Numbers" ], "current_concepts": [ "Complex Number Arithmetic", "Equality of Complex Numbers" ] } ## Solve Equation A for x and y $$ \begin{aligned} (x + yi) + (4 - 7i) &= 3 - 4i \ (x + 4) + (y - 7)i &= 3 - 4i \ x + 4 = 3 &\implies x = -1 \ y - 7 = -4 &\implies y = 3 \end{aligned} $$ ## Solve Equation B for x and y $$ \begin{aligned} (x + yi) - (-6 + 14i) &= 18 + 2i \ (x + 6) + (y - 14)i &= 18 + 2i \ x + 6 = 18 &\implies x = 12 \ y - 14 = 2 &\implies y = 16 \end{aligned} $$ ## Question 1 In equation A, $x =$ -1 and $y =$ 3. ## Question 2 In equation B, $x =$ 12 and $y =$ 16. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Number Arithmetic" ] }

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Question

Explanation:

Solve Equation A for x and y

Solve Equation B for x and y

Answer:

Question 1

Question 2