A System With Conjugates | Problem 341

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[@SweetSorrow777]

2nd method is much simpler, but I used the 1st one because more straightforward even if it's a pain in the butt.

[@mcwulf25]

I used the second method except that I took the conjugate of the second equation. Easy to do it mentally.

[@-wx-78-]

Unicode has combining diacritical marks (mostly in U+0300…036F range), conjugate w̅ can be written as “w” followed by +0305 on numpad with Alt depressed (in Windows).

[@aplusbi]

Thanks. For some reason that did not work for me. Could you copy and paste here, maybe?

[@-wx-78-]

@@aplusbi Somehow my reply containing alphabet with overbars was eaten by CZcams. 😉
Method is simple: type the letter, press and hold “Alt”, type “+” “3” “0” “5” on _numeric keypad_ then release “Alt”. Alternatively, you may use “Character Map” application: select “Arial Unicode MS” font (for example), search for “combining” in Unicode character set (or go straight to Unicode 0305).

[@NadiehFan]

@@aplusbi There are precomposed unicode characters for vowels with a macron such as ā since these are used to indicate long vowels, but there are no such precomposed unicode characters for w and z with a macron so you have to compose these yourself.
You can either use U+0304 Combining Macron:
w̄ z̄
or U+0305 Combining Overline:
w̅ z̅
The alignment of the macron or overline on top of the base character may not be perfect on your display, unless your operating system uses some smart font rendering technology which automatically takes care of this. Of course, the alignment of precomposed unicode characters such as ā is always perfect because this is just a single complete character in a unicode font.

[@scottleung9587]

I used the first method.

[@IITDREAMresonance]

Great video
I would love to see you add more questions at a higher frequency of upload
the work you are doing is awesome i hope you keep up the good work

[@aplusbi]

Thanks! 😮 higher frequency?

[@IITDREAMresonance]

@@aplusbi Yep i mean i want more of your new content and a lot of it as i watch almost every new video of yours

[@SALogics]

Nice explanation ❤❤

[@aplusbi]

Thank you! 😍

[@phill3986]

✌️👏😎👍👍😎👏✌️

[@NadiehFan]

Third method. We can use that z + z̅ = 2·Re(z) and z − z̅ = 2i·Im(z). Adding both equations and subtracting the second equation from the first gives
2·Re(w) + 2i·Im(z) = 8 − 2i
2·Re(z) − 2i·Im(w) = −2 + 6i
From the first equation we get R(w) = 4, Im(z) = −1 and from the second equation we get Re(z) = −1, Im(w) = −3, so z = −1 − i, w = 4 − 3i.

[@aplusbi]

Nice!

[@user-sx6vo6ne5f]

też tak zrobiłem !