<p>Awesome answer. </p>
<p>Do you put on your socks or your shirt first?</p>
<p>Should you keep the tissue box if there’s only one tissue left?</p>
<p>Do you wash your body or shampoo/condition your hair first?</p>
<p>Why am I not getting any work done?</p>
<p>HarryJones- does that have anything to do with De Moivre’s Theorem?</p>
<p>(cos x + i sin x)^n = (e^ix)^n = e^i(nx) = cos nx + i sin nx</p>
<p>Is that what you were asking?</p>
<p>
If you want to know why e^(ix) = cos x + i sin x, look at the infinite series of e^x, sin x, cos x. Substitute x with ix in the e^x infinite series, and group all the x and ix terms separately. You’ll see that the x terms form the cos x infinite series and the ix terms form the sin x infinite series.
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<p>and why their infinite series are relatable has to do with the fact that the functions’ derivates all display periodicity (that is the underlying connection, i think).</p>
yvettec
February 21, 2011, 8:04pm
106
<p>My cousins live in Australia, and yep, Christmas in the summer! Santa dresses in a bathing suit!</p>