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<div>I don't much care, I don't want to define my own math, I just want to know why we mix the real and imaginary parts of a product in one specific case.</div>
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<div>Z1*Z2=r1r2(cos a + isin a)(cosb + isin b)</div>
<div>= r1r2 (cosa*cosb)-(sina*sinb) + i(sina*cosb + cosa*sinb)</div>
<div>= r1r2 (cos(a + b) + isin(a + b))</div>
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<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">You could indeed say that "entity of your choice = 1/0". But you need a<br>compelling reason why such a quantity is useful, and various proofs on how
<br>it is derived and used. All math depends on certain assumptions and those<br>assumptions are different in different circumstances - aka Euclidian<br>geometry and topology.<br><br>Actually, you can say 1+2 = 12 ... and if you are putting together a
<br>string in a programming language, that makes sense and is useful, it is a<br>valid operation. Many object oriented programming languages let you<br>redefine basic symbols such as "+ - * /". But string addition wouldn't be
<br>very helpful for doing audio math calculations.<br><br>So if you want to define your own i, go ahead, but don't you think your<br>calculations are going to turn out better if you follow the normal math<br>definitions?
<br><br>~David<br><br>> What I'm getting at is that expressing rotation as complex numbers is no<br>> different than using cartesian coordinates. Why, when you multiply two<br>> points, would one of the multiples turn negative?
<br>> I see no reason you couldn't say i = 1/0. Then 4*0*i=4. That makes as much<br>> sense.<br>><br><br></blockquote></div><br><br clear="all"><br>-- <br>"It is not when truth is dirty, but when it is shallow, that the lover of knowledge is reluctant to step into its waters."
<br>-Friedrich Nietzsche, "Thus Spoke Zarathustra"