sqrt(i)

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bprp #shorts

[catholicpenguin]

”And we do not need to rationalize the denominator because skdfkenrleörkwl”

[aryanbansal]

but my friends dont know what a square root is 😂😂😂

[bhargavpatel]

Me after doing all this hard work ...
My friend : why didn't you simply write 'i' in its euler form that is e^(i×pie/2)
Me : 😰😰😰😰😰😰😰😰😰😰😰😰😰😰😰😰😰😰😰😰

[kO_EC]

He is @blackpenredpen right ??? He started this new channel?? Any reason ?? He isn't even following this channel in his older channel ..

[chinjunyuan]

0:41
We do not have to rationalize the denominator because? I couldn't hear it

[tomatrix]

Wow I like the binomial square radical trick bprp

[derivatives_of_the_nature]

Maybe using De Moivre’s theorem is better.

[shurjoaunibar]

Lol, I watched Dr. Peyam's e^π vs. π^e video. He did #rap but literally every video you make are raps too! Even the ASMR videos...

[hazarkeshoeshain]

I can buy them a pint of beer and they will still be more impressed than this. But, unfortunately, I don't have any friends. 😔

[stevefan]

so the geometric interpretation of it is its 45 degree on both x and y axis? this kinda fits square root so uh...

[ImMuppt]

My teacher gave me this on an algebra exam, as a root from a polynomio, and I knew that this had many represantations but I used it as it shows. My intuition said me that it was ok, in fact I came up with the same result as in the video (on my side notes), but I discard it because there was no need for it. Furthermore, is it necessary to express it in the form of a+bi always? Or it depends on the problem?

[dilishagurung]

Sir you are absolutely like mine maths sir he also teaches in that same way but we say him to speak slower.

[leonardobarrera]

I had to see 4 times to understand!!!!

[emekdulgeroglu]

It is easier if you make it (e^iπ/2)^(1/2) = e^iπ/4

[Avighna]

Or:

sqrt(i) = a+bi
i = a^2-b^2+2abi
On marching up coefficients, a^2-b^2 = 0, 2ab = 1

From a^2-b^2=0, a = b
2a^2 = 1
a = 1/sqrt(2) = b

Therefore, sqrt(i) = (1 + i)/sort(2)

This method is more general and works for any rational root of i. It also works for finding the square root of any complex number (both of the above things with only the quadratic formula)

[prabhdensingh]

How did you get from sqrt(0+2sqrt(-1/4)) to sqrt(1/2) + sqrt(-1/2)???

[simantakumarbhattacharyya]

Why don't we simply use the Euler form...then convert back to polar form

[archanamittal]

can we write it as :
(1+i)/2 = √i ??

[martinphipps]

Wait.

We can write I = e^(i pi/2).

This is because e^(I x) = cos x + i sin x and cos pi/2 = 0 and sin pi/2 = 1.

So sqrt i = e^(i pi/4) = cos (pi/4) + i sin (pi/4). Simple.

[XDriftwave]

Theres a somewhat easier solution
sqrt(i) = sqrt(e^i pi / 2)
= e^i pi/4
= cos(pi/4) + isin(pi/4)
= sqrt2/2 + i sqrt2/2