<span>–9x(5 – 2x)
= -45x + 18x^2
= 18x^2 - 45x
answer
</span>18x^2 - 45x
Answer:
The answer is below
Step-by-step explanation:
Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:
![z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1](https://tex.z-dn.net/?f=z_1%3Dr%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D%28cos%28%5Cfrac%7B%5Ctheta%20%2B2k%5Cpi%7D%7Bn%7D%20%29%2Bisin%28%5Cfrac%7B%5Ctheta%20%2B2k%5Cpi%7D%7Bn%7D%20%29%29%2C%5C%5Ck%3D0%2C1%2C2%2C.%5C%20.%5C%20.%2Cn-1)
Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:
![z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\](https://tex.z-dn.net/?f=z_%7Bk%3D0%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%280%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%280%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D0%7D%3D3%5Bcos%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%29%5D%5C%5C%5C%5Cz_%7Bk%3D1%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%281%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%281%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D1%7D%3D3%5Bcos%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%29%5D%5C%5C%5C%5C)
![z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]](https://tex.z-dn.net/?f=z_%7Bk%3D2%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%282%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%282%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D2%7D%3D3%5Bcos%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%29%5D%5C%5C%5C%5Cz_%7Bk%3D3%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%283%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%283%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D3%7D%3D3%5Bcos%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%29%5D)
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Answer:
Its A.
Step-by-step explanation:
Can u stop reporting my answers!!??
They definitely can be positive they can be negative and they can have an absolute value but I would choose they both can be positive and negative