in which quadrant is the number $6 - 8i$ located on the complex plane?

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Question

in which quadrant is the number $6 - 8i$ 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 Plane Representation" ], "new_concepts": [], "current_concepts": [ "Complex Plane Representation", "Complex Numbers" ] } ## Identify the real and imaginary parts of the complex number $$ z = 6 - 8i \implies \text{Re}(z) = 6,\quad \text{Im}(z) = -8 $$ ## Determine the corresponding coordinates on the complex plane $$ (x, y) = (6, -8) $$ ## Determine the quadrant of the coordinates $$ x > 0 \text{ and } y < 0 \implies \text{Quadrant IV} $$

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{ "elements": [ { "type": "point", "params": [[6, -8]], "properties": { "name": "6 - 8i", "size": 4, "color": "#8C55F2", "withLabel": true } } ], "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 of the complex number

Determine the corresponding coordinates on the complex plane

Determine the quadrant of the coordinates

Answer: