Simplify Complex Number Fraction

AI Thread Summary
To simplify the complex number fraction \(\frac{(cos60 - isin60)^5 * (cos45 - isin45)^3}{(cos15-isin15)^7}\), it is recommended to convert each term into exponential form using \(e^{-ix} = cosx - isin x\). This transformation allows for easier manipulation through the laws of exponents. After rewriting the expression in terms of \(e\), apply exponent rules to simplify the overall fraction. Following these steps should lead to a clearer solution. The process emphasizes the utility of exponential notation in handling complex numbers.
FelixISF
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Homework Statement



\frac{(cos60 - isin60)^5 * (cos45 - isin45)^3}{(cos15-isin15)^7}


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The Attempt at a Solution



I have had several tries so far, but simply do not know what to do. Would somebody be so kind and simplify this expression step by step. I couldn't find any solved problems like this on the internet and am lost!


Thanks!
 
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Use
e-ix=cosx - isinx
to simplify everything into base e, then use laws of exponents, and you should be able to come to an answer.
 
Last edited:
Thanks!
 

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