To multiply the imaginary number i, we still can use the product rule for exponents. When we multiply, we get
![i^{0+1+2+3+4}=i^{10}](https://tex.z-dn.net/?f=i%5E%7B0%2B1%2B2%2B3%2B4%7D%3Di%5E%7B10%7D)
.
Now, simplifying this might seem formidable at first. But, let's start working through different powers of i.
![i^0=1\\i^1=i\\i^2=-1\\i^3=-i\\i^4=(-1)(-1)=1](https://tex.z-dn.net/?f=i%5E0%3D1%5C%5Ci%5E1%3Di%5C%5Ci%5E2%3D-1%5C%5Ci%5E3%3D-i%5C%5Ci%5E4%3D%28-1%29%28-1%29%3D1)
Notice that
![i^4=1](https://tex.z-dn.net/?f=i%5E4%3D1)
. That means that any power that is a multiply of four will also be 1. For instance,
![i^8=1,\ i^{12}=1](https://tex.z-dn.net/?f=i%5E8%3D1%2C%5C%20i%5E%7B12%7D%3D1)
, and so on...
If we rewrite
![i^{10}](https://tex.z-dn.net/?f=i%5E%7B10%7D)
with this in mind, we can break it down into smaller pieces and simplify.
The answer is B.
<h3>
Answer:</h3>
Sarah: 18
Brother: 24
<h3>
Step-by-step explanation:</h3>
The difference in ratio units is 4-3 =1. The difference in years is 6, so 1 ratio unit stands for 6 years.
Multiplying by 6, we have ...
... Sarah : Brother = 3·6 : 4·6 = 18 : 24
Sarah is 18; her brother is 24.
As h increases 80/h decreases . When h approaches infinity 80/h approaches zero.
Answer:
A. 134. 83
Step-by-step explanation:
1) 5(4/3)^(8-1) / (4/3-1)
2) 5(9.98872-1) / (1/3)
3) 44.9436 / (1/3)
4) 134.83
Answer:
203.20 millimeters
Step-by-step explanation:
StartFraction 8 inches Over question mark millimeters EndFraction = StartFraction 40 inches Over 1,016 millimeters
8 inches / ? Millimeters = 40 inches / 1,016 millimeters
8 × 1,016 = ? × 40
8,128 = 40?
Divide both sides by 40
? = 8,128 / 40
= 203.20
? = 203.20 millimeters
There are 203.20 millimeters in 8 inches