All Powers Of i (iota) #maths

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[sayanlaha]

The powers of i in general form - 4n+0, 4n+1, 4n+2, 4n+3 is according to the Division algorithm...

[lazyshadow]

Or, if we do it simpler, we can say that:
i^3 = -i
i^333 = (i^3)^111 = -i
i^666 = (i^333)^2 = -1

Always remember that this repeats for every exponent of i:
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
...
such that:
i^5 = i
and i^6 = -1
and so on...

It doesn't matter how big the number is, just look at the end of the exponent (the last two numbers)

[NerfPsycho]

i^(4n) = 1:
i^(4 × 1) = i^4 = i^2 × i^2 = -1 × -1 = 1

i^(4n + 1) = i:
i^(4 × 1 + 1) = i^5 = i^4 × i = 1 × i = i

i^(4n + 2) = -1:
i^(4 × 1 + 2) = i^6 = i^4 × i^2 = 1 × -1 = -1

i^(4n + 3) = -i:
i^(4 × 1 + 3) = i^7 = i^4 × i^2 × i = 1 × -1 × i = -1 × i = -i

Therefore i^666 = i^(4 × 166 + 2) = -1 (according to the rule)

[JealousNobody]

The defenition of is is i^2 = -1. Sqrt(-1) is not only i but also -i

[ScienceSpider-sigma]

i * i = -1
-1 * i = -i
-i * i = 1
1 * i = i

[bhupendrakumarchawda]

This is the only video i could understand

[JustForFun-qvhy]

i^666 = -1
Shortcut method : add power 6+6+6=18
Divide 18 with 4 quotient= 2, take 2 as the power of I
i^2 = -1
Therefore, i^666 = i^2= -1

[RedRad]

In order to know if 666 is divisible by 4, you only need to check the last two digits - 66.
64 is a multiple of 4, therefore i^64 = 1.
It follows that i^664 = 1, therefore
i^666 = (i^664) * (i^2) = 1 * (-1) = -1

[narfidort]

4の倍数は下二桁を見れば分かります
66=64+2=16*4+2そのため余りは2です
これは100=25*4であることに基づきます

[sonugamingyt]

It's simple the value to the power of i is even so if its multiple of 4 then the answer is 1 if its not a multiple of 4 but even then its a multiple of 2 so answer is -1.

[xXPrime_MasterXx]

i^n
If n =
0(mod 4) = 1
1(mod 4) = i
2(mod 4) = -1
3(mod 4) = -i

666(mod 4)=2 so the ans will be -1

Full explanation :
•Mod of x means divide any number, lets say n and the remainder will be the answer.
6(mod 2)=0 5(mod 3)=2
4(mod 4)=0

•The i's in the video shows what answer will show if u multiply i or √-1.
It will repeat itself after four times

Thats why theres is no i^4n+4 because it will be the same as i^4n because 4 is a multiple of 4. And so on.

•I used mod to find the answer because it repeats in a loop right? So i need to find what place in the loop 666 will be.

[НикитаПарфенов-зб]

In fact is correct to write it as: i ² =1 because i= √-1 and -i= √-1

[AnkurSingh-wypl]

Just divide with 4 and three remanider three cases❤

[tacobender]

You spin me right round baby right round like a record baby.

[noname-edun]

I don't understand this concept. can you please explain

[whoff]

rotating around the midst of the imaginary plain ...
round and round and round ... forever...

[Sonu-Jadhav]

66/4
Then Raimander is 2 so that
i^2= -1
It's based on number system chapter. This method is helpful because it's take less consume time.
And for govt. Exam

[nikhil_hu]

i^2 (i^664) = -1 explanation i^664 is the multiple of 4 so it became 1 and i^2 is -1 so the answer is here thank u

[afafn]

666%4=166.5
166=n
166x4=664
666-664=2
666=4x166+2
i⁶⁶⁶=i⁴•n+²=-1

[justdontbeordinarymydude]

music : bgnzinho-murder ((slowed reverb))