Originally published at: https://boingboing.net/2019/02/19/learn-the-square-root-of-i-bo.html

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This is a wonderful and amazing thing and makes my inner math geek very happy.

I was born as a defective unit. Maths are somehow more complicated for me than for some people. I always feel dumb, since my brother is way smarter than me, and he always teases me. And I think I’m pretty smart, don’t get me wrong, but numbers are out of my league.

Bah. I seriously can’t add 1+1 in my head and get 2. Make a proof of it that is no problem (or was when I was studying it). Higher math has little to do with numbers.

I pull out my smart phone and use the calculator all the damn time. Math I can do, but arithmetic no fucking way.

Is it me or does “beating the Euler out of it” sound… *naughty*?

Anyway, I couldn’t prove 1+1=2 if my life depended on it.

Mathematical demonstrations are my blind spot.

I managed non-linear partial differential equations and the math behind finite element methods and whatnot when I got my degree; it was work but it wasn’t a problem. But don’t ask me to prove anything.

I’m an engineer, just give me the tools and let me work with them.

I trust mathematicians.

Is it (1+i) / sqrt(2)? Did I remember it right?

yes Boundegar…and the other one…

Just halve the angle on the unit circle, and remember the 1, 1 over root 2, 1 over root 2 triangle… and remember there must be another solution 180 degrees away…

The square root of Bob Ross is a kittie?

Interesting material online on quaternions, and a surprising amount of drama about octonions, once you start looking.

Agreed. Calculations are but a tiny part of the wonder that is Mathematics. The only reason that i can do arithmetic to the small extent that i can is because i’ve gotten so much practice having to do it while teaching higher math.

This looks like a great channel . Thanks for showing it to us !

Perhaps the next installment will explain how e^{π i} = -1

No, nothing can ever, ever explain (much less mathematically prove) this.

That should actually be pretty clear from this video…

(bearing in mind that cos(π)=-1 and sin(π)=0)

If you like questions like the one in the OP there are plenty of them answered on this channel

Although not in the same style.

The best explanation I’ve seen for that related it to rotational angles in the complex plane. This might be the one:

https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

She looks like she loves her maths!

But it all looks really easy when someone else is doing the work.

This Hidden Brain episode: Close Enough: The Lure Of Living Through Others explores why watching videos of other people doing stuff is so attractive.

Euler’s formula is a big gun to bring out for this little problem. Just write (a+bi)^2 = ±i, solve for a and b, and you’re there.

Crap, here comes that unsettling feeling again…

Obligs:

That was literally me while trying to help my kid with ‘common core.’

O_o