what is the sum of $12 - 5i$ and $-3 + 4i$?

- $-16 + 63i$
- $9 - i$
- $9 - 9i$
- $15 - 9i$

Question

what is the sum of $12 - 5i$ and $-3 + 4i$?

- $-16 + 63i$
- $9 - i$
- $9 - 9i$
- $15 - 9i$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Complex Number Operations" ], "new_concepts": [], "current_concepts": [ "Complex Number Operations", "Complex Number Addition" ] } ## Identify the given complex numbers Using the *Complex Number Operations* knowledge point $$ \begin{aligned} z_1 &= 12 - 5i \ z_2 &= -3 + 4i \end{aligned} $$ ## Add the real and imaginary parts Using the *Complex Number Operations* knowledge point $$ \begin{aligned} z_1 + z_2 &= (12 - 5i) + (-3 + 4i) \ &= (12 - 3) + (-5 + 4)i \ &= 9 - i \end{aligned} $$

(A) $-16 + 63i$

(B) $9 - i$

(C) $9 - 9i$

(D) $15 - 9i$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Number Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given complex numbers

Add the real and imaginary parts

Answer: