I 23
Please help me make 23 easier? 3
To remember,
I 0 = 1
i 1 = i
i 2 = 1
i 3 = i
i 4 = 1
i 5 = i
Etc ...
One trick you can do is divide the exponent by 4 and if it ends in a decimal,
In 0.25
0.5 is 1
0.75 i
No decimal place is 1.
So i 23 = i
4/23 = 5.75
Make I 23 easier
There are two possible answers, and it all depends on whether you get a complex number or not.
Otherwise i 23 is just i 23.
If you have already done this and assume that I am I 2 = 1, see below:
i 4 = 1 then the multiple of i 4 = 1
I 23 = I 20 x I 3
Now i 20 = 1 again
i 23 = i 3 = i 2 x i
Now i 2 = 1 (this is the definition)
I 23 = i 3 = 1 x i = i
So i 23 = i ..... as long as it's a complex number i, not a normal i!
Feel it:
i = square (1)
i 2 = (square root (1)) 2 = 1
i 3 = i * i 2 = i
I 4 = I * I 3 = I 2 = 1
I 23 = I (20 + 3)
= me 20 * me 3
= (i 4) 5 * i 3
= 1 * I 3
= میں
i 23 = (i 3) (i 20) = (i 3) ((i 4) 5) = (i 3) (1 5) = (i 3) (1) = i 3
i 23 = i 3 = (i 2) (i) = 1 (i) = i
Then
i 23 = i
I 23
I 23
I 23 = i (23 mod 4) = i 3 = i
I 23 = I 24 * I 1
For the properties of imaginary units:
i 24 = 1
i 1 = i
Therefore:
i 23 = i
I to 23. In its simplest form.
I repeat at 5, so i 23 = i 3
Square (1) (square (1)) = 1
1 (square (1)) =
Square (1) = I.
