Answer:
The correct option is C.
Step-by-step explanation:
The given complex number is
![z=64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])](https://tex.z-dn.net/?f=z%3D64%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29)
We need to find the third root of the given complex number.
![z^{\frac{1}{3}}=(64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}]))^{\frac{1}{3}}](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%2864%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![z^{\frac{1}{3}}=64^{\frac{1}{3}}(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D64%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
De moivre's theorem:
where, n is an integer.
Using de moivre's theorem, we get
![z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}\times \frac{1}{3}]-i\sin[\frac{\pi}{7}\times \frac{1}{3}])](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5D%29)
![z^{\frac{1}{3}}=4(\cos[\frac{\pi}{21}]-i\sin[\frac{\pi}{21}])](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B21%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B21%7D%5D%29)
Therefore the correct option is C.
Answer:
I want to say 50 cars
Step-by-step explanation:
If i am correct, there are more cars than people overall:
tenants to cars
3:5
so when you have 30 tenants you can multiply the cars by ten because that is what you did on the other side.
Answer:
Step-by-step explanation:
<u>Step 1: Make an equation</u>
<u />
<u>Step 2: Cross multiply</u>
<u />
<u>Step 3: Divide both sides by 32</u>
<u />
Answer:
Answer:
The answer is 20
Step-by-step explanation:
Can i have brainiest
A' is (-12, 6)
B' is (0,6)
C' is (3, -3)
D' is (-9, -3)
Hope this helps!
