perform the indicated operations & simplify.

add: $(5 - 13i) + (20 + 4i)$
sum =

subtract: $(5 - 13i) - (20 + 4i)$
difference =

Question

perform the indicated operations & simplify.

add: $(5 - 13i) + (20 + 4i)$
sum =

subtract: $(5 - 13i) - (20 + 4i)$
difference =

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Complex Numbers", "Complex Number Addition", "Complex Number Subtraction" ] } ## Add the complex numbers $$ \begin{aligned} \text{sum} &= (5 - 13i) + (20 + 4i) \ &= (5 + 20) + (-13 + 4)i \ &= 25 - 9i \end{aligned} $$ ## Subtract the complex numbers $$ \begin{aligned} \text{difference} &= (5 - 13i) - (20 + 4i) \ &= 5 - 13i - 20 - 4i \ &= (5 - 20) + (-13 - 4)i \ &= -15 - 17i \end{aligned} $$ ## Question 1 sum = $25 - 9i$ ## Question 2 difference = $-15 - 17i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

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Question

Explanation:

Add the complex numbers

Subtract the complex numbers

Answer:

Question 1

Question 2