Canonical URI: https://w3id.org/kmath/textbook_solution/chunjae_hong_solution_p151_p092_performance_01
| rdf:type | math:TextbookSolution |
|---|---|
| rdfs:label | 천재홍 p092 수행 과제 1 풀이 |
| rdfs:comment | 천재홍 공통수학1 정답 및 풀이 p151의 p092 수행 과제 1 풀이. |
| math:answerText | \(\omega^2=\overline{\omega}\) |
| math:explanationText | 방법 1. \(\omega^2=\left(\frac{-1+\sqrt3 i}{2}\right)^2 =\frac{-2-2\sqrt3 i}{4}=\frac{-1-\sqrt3 i}{2}=\overline{\omega}\). \(\omega\)와 \(\overline{\omega}\)가 바뀌어도 \(\omega^2=\overline{\omega}\)가 성립한다. 방법 2. \(\omega+\overline{\omega}=-1\), 즉 \(\omega=-1-\overline{\omega}\). \(\omega\)는 이차방정식 \(x^2+x+1=0\)의 허근이므로 \(\omega^2+\omega+1=0\). 따라서 \(\omega^2=-\omega-1=-(-1-\overline{\omega})-1=\overline{\omega}\). |
| math:hasFigure | problem_figure:chunjae_hong_p092_performance_omega_methods |
| math:mappingConfidence | 1.0 |
| math:pageStart | 151 |
| math:problem | textbook_problem:chunjae_hong_vision_p092_performance_01 |
| math:reviewStatus | reviewed |
| math:solutionKind | worked_solution |
| math:usesSolutionPattern | solution_pattern:complex_number_algebra |
| math:usesSolutionPattern | solution_pattern:roots_coefficients_symmetric_expression |