1 • 1 + i • i = 1 + (-1) = 0 = 0 • 0
Pythagoras holds, provided there's a 90° angle at A.
this post was submitted on 29 Nov 2024
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I'm so angry at people who think that distances can be imaginary.
You're mad at mathematicians for constructing complex valued metrics? It's all just formalism, nothing personal.
Omg, yes. This is horrible. :)
When talking about AC power, some of the power consumed doesn't actually produce real work. It gets used in the generation of magnetic fields and charges in inductors and capacitors.
The power being used in an AC system can be simplified by using a right triangle. The x axis is the real power being used by resistive parts of the circuit (in kilowatts, KW). The y axis is reactive power, that is power being used to maintain magnetic fields and charges (in kilovolt-amperes reactive, KVAR). And the hypotenuse is the total power used by the circuit, or KVA (kilovolt-amperes).
Literal side note: they're all the same units, but the different sides of the triangle are named differently to differentiate in writing or conversation which side of the power triangle is being talked about. Also, AC generator ratings are given in KVA, so you need to know the total impedance of your loads you want to power and do a bit of trig to see if your generator can support your loads.
The reactive component of AC power is denoted by complex numbers when converting from polar coordinates to Cartesian.
Anyways, I almost deleted this because I figured your comment was a joke, but complex numbers and right triangles have real world applications. But power triangles are really just simplifications of circles. By that I mean phasors rotating in a complex plane, because AC power is a sine wave.
Please be careful with two different things. Complex numbers have two components. Distances don't. They are scalars. The length of the vector (0,1) is also 1. Just as a+bi will have the length sqrt(a^2 + b^2). You can also use polar coordinates for complex numbers. This way, you can see that i has length 1, which is the distance from 0.
The triangle in the example above adds a vector and a scalar value. You can only add two vectors: (1,0) + (0,1) which results in (1,1) with the proper length. Or you can calculate the length/distance (absolute values) of the complex numbers directly.
Its another classic case of Euler's Identity
Never been together with people and still felt alone?
But that's not the definition of the absolut value, I.e. "distance" in complex numbers. That would be sqrt((1+i)(1-i)) = sqrt(2) Also the triangle inequality is also defined in complex numbers. This meme is advanced 4-4*2=0 Works only if you're doing it wrong.
I kept seeing this pop up recently, and I finally understand it: it's an introductory problem in Lorentzian general relativity.
AB is a space-like line, while AC is a time-like line. Typically, we would write AC as having distance of 1, but with a metric such that squaring it would produce a negative result. However it's similar to multiplying i to the value.
BC has a distance of 0, but a better way of naming this line would be that it has a null interval, meaning that light would travel following this line and experience no distance nor time going by.
I'm sure PBS Spacetime would explain all of this better than me. I just woke up and can't bother searching for the correct words on my phone.
I get it, it's projected on a comlplex sphere. B and C are the same point
please stop making it make sense
It gets worse once you start doing trig on it
funny Interpretation: in the complex plane, the imaginary axis is orthogonal to the real axis. so instead of the edge marked with i (AC), imagine an edge of length 1 orthogonal to that edge. It would be identical to AB, so ~~AC~~ CB is 0.
Maybe the problem is constructing a metric that makes this diagram true. Something like d(x,y) = | |x| - |y| | might work but I'm too lazy to check triangle inequality.