How to proceed ahead what is the meaning of maximum of minimum value here graphically? | Mathematics | Page 1

fringe parcel Mar 2, 2025, 5:59 AM

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lilac compassBOT Mar 2, 2025, 5:59 AM

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fringe parcel

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surreal phoenix Mar 2, 2025, 6:01 AM

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fringe parcel

I don't know. There's no total ordering on the complex numbers.

fringe parcel Mar 2, 2025, 6:01 AM

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so how do i proceed ahead in this question?

hasty oxide Mar 2, 2025, 6:11 AM

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surreal phoenix I don't know. There's no total ordering on the complex numbers.

yes, and $z(1+i)+\overline{z}(1-i)\in\bR$

north merlinBOT Mar 2, 2025, 6:11 AM

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idontknowtherules

surreal phoenix Mar 2, 2025, 6:12 AM

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hasty oxide yes, and $z(1+i)+\overline{z}(1-i)\in\bR$

Fair. @fringe parcel

fringe parcel Mar 2, 2025, 6:13 AM

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surreal phoenix Fair. <@860408741936627714>

bruh i m not getting still 😭

surreal phoenix Mar 2, 2025, 6:13 AM

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Or is it?

hasty oxide Mar 2, 2025, 6:13 AM

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surreal phoenix Or is it?

it is

surreal phoenix Mar 2, 2025, 6:14 AM

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Ah, right.

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I made a mistake in the algebra, I see it plainly now.

hasty oxide Mar 2, 2025, 6:14 AM

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you can proceed

fringe parcel Mar 2, 2025, 6:14 AM

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how to ?

surreal phoenix Mar 2, 2025, 6:15 AM

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fringe parcel how to ?

As idontknowtherules said, Q is a subset of R.

surreal phoenix Mar 2, 2025, 6:15 AM

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hasty oxide you can proceed

Wait, hold on, no, Q isn't a subset of R.

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That is, the set Q in the problem, not the set of rational numbers.

surreal phoenix Mar 2, 2025, 6:15 AM

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fringe parcel how to ?

Forget what I just said, that's wrong.

fringe parcel Mar 2, 2025, 6:16 AM

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ok

surreal phoenix Mar 2, 2025, 6:16 AM

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fringe parcel ok

That said.

hasty oxide Mar 2, 2025, 6:16 AM

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surreal phoenix Wait, hold on, no, Q *isn't* a subset of R.

so?

surreal phoenix Mar 2, 2025, 6:16 AM

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hasty oxide so?

...so then the issue of ordering on C returns.

hasty oxide Mar 2, 2025, 6:16 AM

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i didn't read the rest of the problem yet gimme a min

surreal phoenix Mar 2, 2025, 6:17 AM

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hasty oxide i didn't read the rest of the problem yet gimme a min

The core question is what does it mean to refer to the "maximum" or "minimum" of a set of complex numbers?

fringe parcel Mar 2, 2025, 6:17 AM

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graphically *

hasty oxide Mar 2, 2025, 6:17 AM

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surreal phoenix The core question is what does it mean to refer to the "maximum" or "minimum" of...

it says

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find when |z-3+2i| is max

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for z in P cap Q

surreal phoenix Mar 2, 2025, 6:18 AM

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Okay.

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So that makes sense.

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@fringe parcel The way it works is that f(z) = |z - 3 + 2i| is a function from C to R that you're to maximize or minimize.

fringe parcel Mar 2, 2025, 6:19 AM

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cant i do it graphically?

surreal phoenix Mar 2, 2025, 6:19 AM

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Specifically on the subset of C that is PnQ.

fringe parcel Mar 2, 2025, 7:29 AM

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surreal phoenix So *that* makes sense.

how do i find z1 and z2 here?

hasty oxide Mar 2, 2025, 8:03 AM

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fringe parcel how do i find z1 and z2 here?

why do you insist on doing it graphically

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isn't that counterintuitive

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if you want to do that, then do it, increasing your work 🔥

fringe parcel Mar 2, 2025, 8:04 AM

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hasty oxide if you want to do that, then do it, increasing your work 🔥

how algebraically then can u tell

hasty oxide Mar 2, 2025, 8:05 AM

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fringe parcel how algebraically then can u tell

Can you find $P\cap Q$?

north merlinBOT Mar 2, 2025, 8:05 AM

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idontknowtherules

fringe parcel Mar 2, 2025, 8:05 AM

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yeah its clear in the image the intersection of both

hasty oxide Mar 2, 2025, 8:06 AM

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bro

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i mean algebraically

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just

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okay let's do it graphically then

fringe parcel Mar 2, 2025, 8:10 AM

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i can proceed algebraically as well just guide me

hasty oxide Mar 2, 2025, 8:11 AM

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fringe parcel i can proceed algebraically as well just guide me

hm you're not willing to do that

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i asked you to find PnQ and you just said "intersection of both" instead of a set

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anyways

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i'll do it graphically just give me a min

hasty oxide Mar 2, 2025, 8:13 AM

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fringe parcel how do i find z1 and z2 here?

|z-3+2i| denotes distance from (3,-2)

fringe parcel Mar 2, 2025, 8:14 AM

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yeh

hasty oxide Mar 2, 2025, 8:14 AM

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fringe parcel how do i find z1 and z2 here?

z1 and z2 are labelled correctly here, and they're both on the line joining (3,-2) and (-2,3), the latter point is teh centre of the circle

fringe parcel Mar 2, 2025, 8:16 AM

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oh yeah i can just find the equation of line

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with two given points

hasty oxide Mar 2, 2025, 8:16 AM

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it passes through the origin 🗣️🗣️

fringe parcel Mar 2, 2025, 8:16 AM

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and later find point of intersection with circle for z1 and with line for z2

hasty oxide Mar 2, 2025, 8:16 AM

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fringe parcel and later find point of intersection with circle for z1 and with line for z2

👍

fringe parcel Mar 2, 2025, 8:17 AM

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hasty oxide it passes through the origin 🗣️🗣️

bro check the diagram

hasty oxide Mar 2, 2025, 8:17 AM

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hm?

fringe parcel Mar 2, 2025, 8:17 AM

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its not passing through origin

hasty oxide Mar 2, 2025, 8:19 AM

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oh right

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y=1-x

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my bad it doesnt pass through the origin

fringe parcel Mar 2, 2025, 8:20 AM

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hasty oxide my bad it doesnt pass through the origin

yeah so thank u for helping me out

hasty oxide Mar 2, 2025, 8:20 AM

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np

fringe parcel Mar 2, 2025, 8:20 AM

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btw how to find algebraically?

hasty oxide Mar 2, 2025, 8:21 AM

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fringe parcel btw how to find algebraically?

it's bounded on both sides

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so that's only half complete

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after that you just bash it

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hmm that's longer

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didn't realize

fringe parcel Mar 2, 2025, 8:22 AM

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gotcha

hasty oxide Mar 2, 2025, 8:22 AM

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anyways dw about that

fringe parcel Mar 2, 2025, 8:22 AM

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yeah

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+close

gleaming craneBOT Mar 2, 2025, 8:22 AM

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fringe parcel +close

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gleaming craneBOT Mar 2, 2025, 8:22 AM

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#How to proceed ahead what is the meaning of maximum of minimum value here graphically?