# EE102 Systems and Signals (Discussion)

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Next: First Order Linear Differential Up: Complex Numbers Previous: Complex Numbers

### Euler's Equation and Applications

Euler's equation states:

Some simple special cases would be:

 : : : :

Euler's equation is very useful in deriving many trigonometric identities. We notice, that

cossin

where denotes complex conjugation.

Hence we get the following formulas:

 cos Re sin Im

Euler's equation is very useful in deriving many trigonometric identities. First let's derive the formulas for the cosine and sine of a sum of two angles. We have

Hence,
 cossin cossincossin coscossinsinsincoscossin

Equating the real and imaginary parts on both sides, we get the identities
 cos coscossinsin sin sincoscossin

Replacing by in the above identities, we get

 cos coscossinsin sin sincoscossin

Using the above two sets of identities, we get

 coscos sinsin sincos

Next: First Order Linear Differential Up: Complex Numbers Previous: Complex Numbers

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Sankaran Panchapagesan
2002-06-05