Answer:
<em>The correct option is C.</em>
Step-by-step explanation:
<u>Root Of Complex Numbers</u>
If a complex number is expressed in polar form as
Then the cubic roots of Z are
![\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_1%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%5Cright%29)
![\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_2%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%2B120%5Eo%5Cright%29)
![\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_3%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%2B240%5Eo%5Cright%29)
We are given the complex number in rectangular components
Converting to polar form
It's located in the second quadrant, so
The number if polar form is
Its cubic roots are
![\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_1%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C%5Cfrac%7B120%5Eo%7D%7B3%7D%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%5Cright%29)
![\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_2%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%2B120%5Eo%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C160%5Eo%5Cright%29)
![\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_3%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%2B240%5Eo%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C280%5Eo%5Cright%29)
Converting the first solution to rectangular coordinates
![z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)](https://tex.z-dn.net/?f=z_1%3D%5Csqrt%5B3%5D%7B2%7D%28%5C%20cos40%5Eo%2Bi%5C%20sin40%5Eo%29)
The correct option is C.
Because they're consecutive, it means that the first one is x, the second one is x+1, the third one is x+2 (x+1+1), and the fourth one is x+3. Because we're given that the sum of all of them is 682, just add all of them together:
x+(x+1)+(x+2)+(x+3)=682
x+x+x+x+1+2+3=682
4x+6=682
4x+6-6=682-6
4x=676
x=676/4
x=169
Thus, the consecutive integers are: 169, 170, 171, 172
Answer:
that is the answer to letter A y=3/10+3
That is the answer to letter B 3
here is the following. no following figure so the answer is none.
Answer:
Step-by-step explanation:
Answer:
interior and exterior
Step-by-step explanation:
i know it cus i might be smart
