st","extracted_subject":"MATH","extracted_chapter":"COMPLEX NUMBERS","extracted_topic":"GEOMETRY OF COMPLEX NUMBERS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2259.png?top_left_x=532&top_left_y=1112&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab321748","slug":"if-zsup2sup-1-z-sup2sup-1-then-z-lies-on-a-","content":"If \\| z² – 1\\| = \\| z \\|² + 1 then z lies on a –","options":[{"_id":"68a3d35c7f15af4716c50988","text":"Circle","sequence":0,"isCorrect":false},{"_id":"68a3d35c7f15af4716c50989","text":"Parabola","sequence":1,"isCorrect":false},{"_id":"68a3d35c7f15af4716c5098a","text":"Ellipse","sequence":2,"isCorrect":false},{"_id":"68a3d35c7f15af4716c5098b","text":"None of these","sequence":3,"isCorrect":true}],"correct_answer":"None of these","explanation":"**Sol**. On putting z = x + iy the equation is same as\n\n\\| x² – y² + 2ixy – 1\\| = x² + y² + 1\n\nŽ (x² – y² – 1)² + 4x²y² = (x² + y² + 1)²\n\nŽ x = 0\n\nŽ z lies on imaginary axis, so (A), (B), (C) are ruled out.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.873Z","__v":0,"vector_store_id":"ce2d7249-30ed-4e9a-a1c9-5b4052f024cc","updated_at":"2024-08-30T21:49:40.873Z","isStarred":false},"params":{"questionSlug":"if-zsup2sup-1-z-sup2sup-1-then-z-lies-on-a-"}}]}]]

Question: If \| z<sup>2</sup> – 1\| = \| z \|<sup>2</sup> + 1 then z lies on a –...

Solution