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Exercise:
Show that the following relations are true: abcliste abc cosomega t frace^iomega t+e^-iomega t abc sinomega t frace^iomega t-e^-iomega ti abcliste

Solution:
abcliste abc e^iomega t+e^-iomega t cosomega t+isinomega t+cos-omega t+isin-omega t Using cos-xcosx and sin-x-sinx we get e^iomega t+e^-iomega t cosomega t+isinomega t+cosomega t-isinomega t cosomega t The expression for cosomega t follows immediately. abc e^iomega t-e^-iomega t cosomega t+isinomega t-cos-omega t-isin-omega t cosomega t+isinomega t-cosomega t+isinomega t isinomega t The expression for sinomega t follows immediately. abcliste
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Exercise:
Show that the following relations are true: abcliste abc cosomega t frace^iomega t+e^-iomega t abc sinomega t frace^iomega t-e^-iomega ti abcliste

Solution:
abcliste abc e^iomega t+e^-iomega t cosomega t+isinomega t+cos-omega t+isin-omega t Using cos-xcosx and sin-x-sinx we get e^iomega t+e^-iomega t cosomega t+isinomega t+cosomega t-isinomega t cosomega t The expression for cosomega t follows immediately. abc e^iomega t-e^-iomega t cosomega t+isinomega t-cos-omega t-isin-omega t cosomega t+isinomega t-cosomega t+isinomega t isinomega t The expression for sinomega t follows immediately. abcliste
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complex numbers, euler formula, exponential
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