除法复数-概念

我假设你们已经知道如何除矩形形式的复数了但是如何除三角形式的复数呢?
这里有两个一般的复数，z1=r (cos + isin) z2=s (cos + isin)我要把这两个除出来，得到一个公式。从z1 / z2开始。它等于rcos + isin scos + isin。你们还记得复数除法的技巧吗就是上下同乘以分母的共轭。所以在这部分，你不用担心s。
分母的共轭是cos - isin。我要把上下相乘。这个乘积，因为它最终会得到一个平方之差最终会得到一个实数。我们来看看。我们有s，我把r / s提出来。我们得到r / s乘以cos + isin乘以cos - isin。等于cos²- i²sin²。然后在上面，我们有cos cos另一项是这两项的乘积。减去i²sin sin。然后是isin cos和- icos sin。 Okay, that's a lot. So, let's take a look at this. This denominator, remember that i squared is -1 so -i squared is +1, this is cosine squared beta plus sine squared beta by the Pythagorean identity, this denominator is 1 and so we're left with just the numerator, r over s times that numerator. So let me copy that up here. z1 over z2 is r over s times and again i squared is -1 so this will become plus sine alpha sine beta. Cosine alpha cosine beta. Cosine alpha cosine beta plus sine alpha sine beta, and then actually I'm going to need a bracket here, plus i times, I'm going to pull the i out of these 2 terms and I'll be left with sine alpha cosine beta minus cosine alpha sine beta. Sine alpha cosine beta minus cosine alpha sine beta. Okay, this is it.
最后，cos cos加上sin sin是什么?这是cos的一个加法公式，对吧?它是差值的余弦。记住，差值的余弦有一个加号。所以它是cos(-)然后加上i乘以这是sin (-)这就揭示了，如果你想除两个数，两个复数你除以它们的模然后减去它们的参数。这是要记住的，要除以两个复数，除模，然后减去它们的参数。