Given a complex number in the form:
![z= \rho [\cos \theta + i \sin \theta]](https://tex.z-dn.net/?f=z%3D%20%5Crho%20%5B%5Ccos%20%5Ctheta%20%2B%20i%20%5Csin%20%5Ctheta%5D)
The nth-power of this number,

, can be calculated as follows:
- the modulus of

is equal to the nth-power of the modulus of z, while the angle of

is equal to n multiplied the angle of z, so:
![z^n = \rho^n [\cos n\theta + i \sin n\theta ]](https://tex.z-dn.net/?f=z%5En%20%3D%20%5Crho%5En%20%5B%5Ccos%20n%5Ctheta%20%2B%20i%20%5Csin%20n%5Ctheta%20%5D)
In our case, n=3, so

is equal to
![z^3 = \rho^3 [\cos 3 \theta + i \sin 3 \theta ] = (5^3) [\cos (3 \cdot 330^{\circ}) + i \sin (3 \cdot 330^{\circ}) ]](https://tex.z-dn.net/?f=z%5E3%20%3D%20%5Crho%5E3%20%5B%5Ccos%203%20%5Ctheta%20%2B%20i%20%5Csin%203%20%5Ctheta%20%5D%20%3D%20%285%5E3%29%20%5B%5Ccos%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%2B%20i%20%5Csin%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%5D)
(1)
And since

and both sine and cosine are periodic in

, (1) becomes
Answer:
20
Step-by-step explanation:
To solve, I converted the fraction to decimals
1.5/(2.25-0.75) X 1.8 = 1.5/1.5 X 1.8 = 1.8
3.2 - 1.20 = 2
3(2/30 - 1/30) = 3(1/30) = 3/30 = 1/10 = 0.1
2(2/64 / 1/16) = 2(32/64) = 2 (1/2) = 1
1.8/0.1 + 2/1 = 18 + 2 = 20
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Answer:
y=7x
Step-by-step explanation:
When finding the slope intercept form using 2 points, we do the following.
y=mx+b (Slope intercept from)
y=7x+b (7 is slope)
Substitute the point
7=7(1)+b
7=7+b
b=0
y=7x