The equation of a line when it's slope is known can be written in the form of complex numbers as
$$z (m+i) + \bar z(m -i) + 2c = 0$$
(you can derive it from $y=mx +c$ form, and for clarity I didn't assume $m-i =A$ and didn't write $2c=B$)
So, it is given to us that
$$
|z|^2+\bar{A}z^2+A(\bar{z})^...
multiplying by e^(ia) basically means the angle with x axis increases by a, without changing the ||. This happens for both lines, and thus the angle between them is the same...
God is dead. God remains dead. And we have killed him. Yet his shadow still looms. How shall we comfort ourselves, the murderers of all murderers? What was holiest and mightiest of all that the world has yet owned has bled to death under our knives; who will wipe this blood off us? What water is there for us to clean ourselves?
@NoseBleed it may not be legal to beat students but if there is nobody suing those teachers beating students, they can still beat students whether it's legal or not.
@NoseBleed the AA postulate states that two triangles are similar if they have two corresponding angles congruent. but i am asking how here that angle is same
The discussion here is not civil and constructive. Please abstain from talking about topics such as violence and drugs. I am putting this room in timeout for an hour for things to cool down.
user435118
16:35
This room was placed in timeout for 1 hour; See message, uncivil and unconstructive conversation
This room was placed in timeout for 1 minute; the topic of this room is "This is the room where we talk about Physics in a friendly way. LaTex in chat math.ucla.edu/~robjohn/math/mathjax.html" - conversation should be limited to that topic.
This room continues to generate flags. This is not tenable.
Generally extended talks about violence and alike are not acceptable, even when in jest.
More broadly it can help to keep the room ontopic.
"This is the room where we talk about Physics in a friendly way."
I do not want to be a hypocrite. My room is also not very on-topic at times. It is alright to veer off-topic in chat, but keep it "family friendly."
It actually can also make sense to be more exact in the scope of the room.
If this is actually not a room about Physics but something else then say so.
I mean rooms are open to everyone. It is strange to have a room about Physics with very little physics.
If somebody walks in here for physics it would be strange surprise.
Anyway the main point is really that SE chat should not be controversial in any way; maybe in any way is to strong, but there should not be any pointless provocations.
It should be kept somewhat professional.
I'll unfreeze the room now, hoping that things will be better going forward.