evaluate $(2-5i)(p+q)(i)$ when $p = 2$ and $q = 5i$.

* $29i$
* $29i - 20$
* $-21i$
* $29$

Question

evaluate $(2-5i)(p+q)(i)$ when $p = 2$ and $q = 5i$.

* $29i$
* $29i - 20$
* $-21i$
* $29$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Number Multiplication", "Complex Number Simplification" ], "new_concepts": [], "current_concepts": [ "Complex Number Multiplication", "Complex Number Simplification" ] } ## Substitute the given values into the expression $$ \begin{aligned} &\text{Given expression: } (2-5i)(p+q)(i)\ &\text{Substitute } p = 2 \text{ and } q = 5i:\ &(2-5i)(2+5i)(i) \end{aligned} $$ ## Simplify the product of the complex conjugates $$ \begin{aligned} &(2-5i)(2+5i) = 2^2 - (5i)^2\ &2^2 - (5i)^2 = 4 - 25i^2\ &4 - 25(-1) = 4 + 25 = 29 \end{aligned} $$ ## Multiply by the remaining factor $$ \begin{aligned} &29 \cdot i = 29i \end{aligned} $$

(A) $29i$

(B) $29i-20$

(C) $-21i$

(D) $29$

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

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QUESTION IMAGE

Question

Explanation:

Substitute the given values into the expression

Simplify the product of the complex conjugates

Multiply by the remaining factor

Answer: