N
ND
Guest
That would be so hard to do.
Nice complex numbers problem (1 Viewer)
- Thread starter maniacguy
- Start date
N
ND
Guest
Just a shit public school.
Interesting problem. Affinity did well. Following might be an improvement.
triangle inequality could also be : |a-b|<=c where a,b,c are sides of triangle.
Consider the triangle whose vertices in the Argand Plane are
1,cis(arg z), and z.
Then using the inequality,
||z-cis(arg z)|-|z-1||<=|cis(arg z)-1|
LHS=||z|-1|-|z-1|| and RHS is < |arg z|
since the arc length is > the chord.
triangle inequality could also be : |a-b|<=c where a,b,c are sides of triangle.
Consider the triangle whose vertices in the Argand Plane are
1,cis(arg z), and z.
Then using the inequality,
||z-cis(arg z)|-|z-1||<=|cis(arg z)-1|
LHS=||z|-1|-|z-1|| and RHS is < |arg z|
since the arc length is > the chord.
Last edited:
I tried. Unfortunately the post didn't register because it claimed I wasn't logged in.Originally posted by enak
maniac: perhaps you would like to edit your first post to make it correct, then people attempting it wouldn't have so much trouble
On the plus side, the discussion of geometric applications of complex numbers is being introduced
This is a very powerful tool to have at your disposal.The solution I'd intended was:
Consider O (0), A(1), B(|z|), Z(z) (Bracketed are the complex nos)
LHS = |||z|-1|-|z-1||
= ||OB-OA|-AZ|
= |AB - AZ|
< BZ
<= arc BZ
= |z||Arg(z)|
= RHS
Without the |z| the RHS doesn't instantly suggest geometry (as it stands the formula l = r*@ is being strongly hinted)
(Stuffing up the problem, though, was a bit worse, especially since it was still a valid result!)
freaking_out
Saddam's new life
no, i mean 100 in 4u maths....
N
ND
Guest
Oh, well turtle did come 1st in the state.
freaking_out
Saddam's new life
so did he get 100 for 4u?
N
ND
Guest
Where were the stats released?
freaking_out
Saddam's new life
yeah, i thought they were kept secret...(well i heard in the physics forum).
redslert
yes, my actual brain
yeah they do keep it a secret!
must have been some guy who heard it from some other guy, who heard it from some other guy, who just thought it was right
must have been some guy who heard it from some other guy, who heard it from some other guy, who just thought it was right
freaking_out
Saddam's new life
lol- "i heard it from a friend of a friend of mine"
4 unit maths is easy only if you view it that way, sure there are some hard questions but if you tackle it as if it is an easier subject than people usually put it to be than youll find it much easier, at the start of the year i wasnt really confident and wasnt doing well, i just decided to make my self think this wasnt hard and that i just had to work a little bit and damn im going through q7 and and almost all of 8 with just a few problems, so your attitude towards the subject in my experience makes a big difference.