Tag Archives: multiplication

Complex multiplication: proof

In my previous post, I claimed that when multiplying two complex numbers, their lengths multiply and their angles add, like this: In particular, this means that there are always different complex numbers whose th power is equal to : they … Continue reading

Posted in geometry, pictures | Tagged , , , , ,

Complex multiplication and roots of unity

If played around with the question from my previous post, you probably found something like the following: That is, as the powers of we get , , and with all possible sign combinations. Of course, since , if we continue … Continue reading

Posted in geometry, pictures | Tagged , , , , , | 4 Comments

Minus times minus is plus

I’ve seen several recent posts wondering about an intuitive explanation for the fact that “a minus times a minus equal to a plus”. I understand why people would wonder about this—the way it’s often taught, it seems to be just … Continue reading

Posted in arithmetic | Tagged , , | 14 Comments

Ways to multiply

Ξ at 360 has a couple of posts (with more to come!) listing a bunch of different algorithms for performing multiplication. Did you even know there was more than one? Would you be surprised to learn that over the years, … Continue reading

Posted in computation | Tagged , ,