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IrishBoy123
 one year ago
complex number
IrishBoy123
 one year ago
complex number

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0for \( z = 2\), prove: \[z^2  4 z  3  \le 15\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[15 \le z^24z3 \le 15 \\ 15+3 \le z^24z \le 15+3 \\ 12 \le z^24z \le 18 \\ 12+4 \le z^24z+4 \le 18+4 \\ 8 \le (z2)^2 \le 22 \\ 0 \le (z2)^2 \le 22 \\ (z2)^2 \le 22 \\ \sqrt{22} \le z2 \le \sqrt{22} \\ \] I wonder if it has anything to do with this I'm still thinking

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I wonder if I take it easy?? Using Triangle in equality, I have \(z^24z 3\leq z^2 +4z+3= z^2 +4z +3)= 2^2 +4*2 +3 =15\)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I think loser's way works awesome

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Thank you. I was doubt myself.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 which are the sides of the triangle??

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0can you draw it pls?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1That is the triangle inequality theorem.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1\(x+y\leq x +y\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0yes, i can see that, it is absolutely marvellous however, i cannot see how we apply it to \[z^2−4z−3\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[z^24z3=z^2+(4z3) \le z^2+(4z3) =z^2+(1)(4z+3) \\ =2^2+1 \cdot 4z+3=4+1 \cdot 4z+3 \\= 4+4z+3 \le 4+4z+3 =4+4 \cdot z+3 \\ =4+4(2)+3=4+8+3=15\] is it the three term thing @IrishBoy123 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1http://mathworld.wolfram.com/TriangleInequality.html triangle inequality can hold for more than two term

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0yep @freckles it is the 3 term thing i can see the basic triangle thing but i am staring at a quadratic in z and it is not so clear

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Well you could apply the triangle inequality twice as I did above

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440897294917:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0right, i need to read some more brilliant, @freckles and @Loser66 much appreciated! i will revert :p

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0and by read, i mean read 'this thread'

freckles
 one year ago
Best ResponseYou've already chosen the best response.1loser was the brilliant one he was like oh lets use triangle inequality

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0"I'm so sorry loser" you could not make this up! good night lovely people! sleep well!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0well, depends on what time zone you are in, i suppose, but......zzzzzzzzz.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0got there! posting a related question. i think i know how to do it now but i am interested in seeing what people have to say.
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