Eric Nicholas K's answer to lim's Junior College 2 H3 Maths Singapore question.
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Part ii
Date Posted:
4 years ago
(c - a)e^-⅓πi
= ce^-⅓πi - ae^-⅓πi
= re^(θ + 4/3π - ⅓π)i - re^(θ - ⅓π)i
= re^(θ+π)i - (- re^(θ - ⅓π + π)i )
= -re^(θ + π - π)i + re^(θ + ⅔π)i
= -re^θi + b
= b - a
= ce^-⅓πi - ae^-⅓πi
= re^(θ + 4/3π - ⅓π)i - re^(θ - ⅓π)i
= re^(θ+π)i - (- re^(θ - ⅓π + π)i )
= -re^(θ + π - π)i + re^(θ + ⅔π)i
= -re^θi + b
= b - a
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