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.
5 plus five plus 1 that's what I could make.(hope it helps!!!)
Answer:
hope it helps ya.
please give me brainliest
If Terri had 5 blouses and 3 pairs of pants, Teri could wear 15 different combinations of clothes. 1 blouse can be worn with any of the three pairs of pants, as for the other 4. 5 * 3 = 15. The answer is 15 combinations.
Answer:
B: y = 2x + 3
Step-by-step explanation:
The 2x is the slope, and the 3 is the y-intercept
The y-intercept is kinda like how far the slope is from zero, but it can only be applied to the y-axis.
The slope is... well... the slope-- like how steep it is. If a slope is 2/1, like in the graph, it will go higher 2 units every 1 unit across. Or, if the slope is 1/4: The slope will go 1 unit higher every 4 units
