<em>The question is not clearly readable, but I'm assuming the expression which makes more sense, so you can have a clue</em>
Answer:
![i^{97}-i=0](https://tex.z-dn.net/?f=i%5E%7B97%7D-i%3D0)
Step-by-step explanation:
<u>Powers of The Imaginary Unit</u>
The imaginary unit i is defined as
The first powers of i are
![i^0=1](https://tex.z-dn.net/?f=i%5E0%3D1)
![i^1=i](https://tex.z-dn.net/?f=i%5E1%3Di)
![i^2=(\sqrt{-1})^2=-1](https://tex.z-dn.net/?f=i%5E2%3D%28%5Csqrt%7B-1%7D%29%5E2%3D-1)
![i^3=i.i^2=-i](https://tex.z-dn.net/?f=i%5E3%3Di.i%5E2%3D-i)
![i^4=i^2.i^2=1](https://tex.z-dn.net/?f=i%5E4%3Di%5E2.i%5E2%3D1)
And so on the cycle repeats every four numbers. To find the value of
we can find the remainder of 96/4=0. So ![i^{96}=i^0=1](https://tex.z-dn.net/?f=i%5E%7B96%7D%3Di%5E0%3D1)
The given expression is
![i^{97}-i](https://tex.z-dn.net/?f=i%5E%7B97%7D-i)
Factoring
![i(i^{96}-1)](https://tex.z-dn.net/?f=i%28i%5E%7B96%7D-1%29)
Since ![i^{96}=1](https://tex.z-dn.net/?f=i%5E%7B96%7D%3D1)
![=i(1-1)=0](https://tex.z-dn.net/?f=%3Di%281-1%29%3D0)
The required value is 0
I believe it would be 12 because 9 min divided by .75 a rotation gets 12 rotations
Answer:
First one
Step-by-step explanation:
.20 is 20% of 100 and there is 5 boxes and 5 times 20 = 100
Answer:
1). x = 81
2). x = 84
Step-by-step explanation:
1). By applying geometric mean theorem in the given triangle,
![\frac{x}{18\sqrt{14}}= \frac{18\sqrt{14}}{56}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B18%5Csqrt%7B14%7D%7D%3D%20%5Cfrac%7B18%5Csqrt%7B14%7D%7D%7B56%7D)
56x = (18√14)²
56x = 4536
x = ![\frac{4536}{56}](https://tex.z-dn.net/?f=%5Cfrac%7B4536%7D%7B56%7D)
x = 81
2). By applying geometric mean theorem,
![\frac{x}{8\sqrt{21}}= \frac{8\sqrt{21} }{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B8%5Csqrt%7B21%7D%7D%3D%20%5Cfrac%7B8%5Csqrt%7B21%7D%20%7D%7B16%7D)
16x = (8√21)²
16x = 1344
x = ![\frac{1344}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1344%7D%7B16%7D)
x = 84