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:
Orientation
Location I think
Step-by-step explanation:
Answer:
7m³ - 11m² + 5m + 17
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
3m³ - 4m² + 8 - (-4m³ + 7m² - 5m - 9)
<u>Step 2: Simplify</u>
- [Distributive Property] Distribute negative: 3m³ - 4m² + 8 + 4m³ - 7m² + 5m + 9
- Combine like terms (m³): 7m³ - 4m² + 8 - 7m² + 5m + 9
- Combine like terms (m²): 7m³ - 11m² + 8 + 5m + 9
- Combine like terms (Z): 7m³ - 11m² + 5m + 17
Hey there! :D
Complementary angles are equal to 90 degrees.
90-41= 49
The compliment is 48 degrees.
I hope this helps!
~kaikers
