in which quadrant is the number $-14 - 5i$ located on the complex plane?

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Question

in which quadrant is the number $-14 - 5i$ located on the complex plane?

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ii
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iv

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Complex Numbers" ], "new_concepts": [ "Complex Plane Representation" ], "current_concepts": [ "Complex Numbers", "Complex Plane Representation" ] } ## Identify the real and imaginary parts $$ \begin{aligned} z &= -14 - 5i \ \text{Re}(z) &= -14 \ \text{Im}(z) &= -5 \end{aligned} $$ ## Determine the corresponding coordinate point $$ (x, y) = (-14, -5) $$ ## Determine the quadrant of the point $$ \begin{aligned} x < 0 &\quad\text{and}\quad y < 0 \ &\implies \text{Quadrant III} \end{aligned} $$

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{ "elements": [ { "type": "point", "params": [[-7, -2.5]], "properties": { "name": "-14 - 5i", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "text", "params": [5, 5, "Quadrant I"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-8, 5, "Quadrant II"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-8, -5, "Quadrant III"], "properties": { "color": "#8C55F2" } }, { "type": "text", "params": [5, -5, "Quadrant IV"], "properties": { "color": "#583C87" } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Plane Representation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the real and imaginary parts

Determine the corresponding coordinate point

Determine the quadrant of the point

Answer: