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Watch the full Doing Things the Hard Way Matt working out (Patreon)

Published:
2024-02-13 19:25:02
Imported:
2026-06

Content

Here is the full working out, complete with some fun behind-the-scenes bits of me doing the long working out for the cube root of i. That said: it's not that long. Or maybe even that fun. You be the judge!

From this main-channel video: https://youtu.be/ErBbyLu-M94

Direct link to the bonus content video: https://youtu.be/EeJV_8OYzqA

Files

2nd Channel Cube Root of i

Comments

The Live Toad

so you're not so fond of the binomial theorem?

Marty S

About halfway through, you wrote the RHS as 1 instead of i. Also, you overlooked the solution a=0, b=-1.

Ewen McNeill

That’s some deep “behind the scenes” content right there. Business slippers, pets, and the “oh, that’s normally off camera so tidying up is still on the todo list” :-) Ewen

Vincent Zalzal

I wonder how many dice are in that jar behind you... asking for a friend.

Bartosz Błaszkiewicz

He didn't overlooked it. He missed it when working out the hard way, but than gave it in a main video. The exact problem is that when you have an equation a^3-3ab^2=0 you cannot divide both sides by a and simplify it like he did. Instead you can take out an a like this: a(a^2-3ab)=0 which gives you condition that either a=0 or a^2-3ab=0. I posted similar comment under his behind the scenes video but I was too lazy to write all equations. Now I'm writing them from memory so sorry if I messed something up. I'm sure I got the gist of it right.

Bartosz Błaszkiewicz

Matt. I have to disagree with you on which root is trivial. -i was not the one that springs to my mind immediately. When I paused your video and tried to work it out in my head the obvious thing for me was to think of this in polar coordinates. The trivial root is the one that has a modulus equal to the cube root of i (cube root of 1 is one) and the angle one third of i (one third of 90° is 30°). The other 2 i worked out by dividing the coordinate system into 12 pizza slices and then counting 1,2,3,4,1,2... starting from the trivial root.

John L

He may not have been teaming with a lot ‘o news about binomial theorem but he did at least give us some cheerful facts about the square of the hypotenuse

UsrBinPRL

What I've learnt from this video is that I need a pair of business slippers.

Marty S

Hey VZ, I really like your MC Escher-like avatar, logo, or whatever you call it!

Marty S

When you are solving a cubic and you only get 2 solutions, that is an oversight. When you divide by something that might be zero, that is an oversight.

Vincent Zalzal

Hey, thanks Martin! I started from the Penrose triangle image from wikipedia, and I edited it with love in good old Paint ;) I like it, I've used it for many years now.