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:
t = 13
Step-by-step explanation:
3 months ------ 4500
6 months ------ x
3/6 = 4500/x
cross multiplation:
3x =27000
x = 9000,or we should have just doubled the wages, since the time doubled
3 months ------ 4500
5 months ------ y
3/5 = 4500/y
3y = 22500
y = 7500
3 months ------- 4500
t months -------- 19500
3/t = 4500/19500 = 3/13
3t = 39
t = 13
Order of Operation is the step by step procedure that you should follow when solving muti-step equations. Its usally abbreviated as:
P arathesis
Example: 2(5+4)
E xponents
Example: 4^8
M utiply
Example: 5x
D ivide
21/3
A dd
Example: 4+9
S ubtract
Example: 78-21
Answer:
1
Step-by-step explanation:
LCD = 1
Equivalent Fractions with the LCD
9 = 9/1
8 = 8/1
6 = 6/1
5 = 5/1
Solution:
Rewriting input as fractions if necessary:
9/1, 8/1, 6/1, 5/1
For the denominators (1, 1, 1, 1) the least common multiple (LCM) is 1.
LCM(1, 1, 1, 1)
Therefore, the least common denominator (LCD) is 1.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
9 = 9/1 × 1/1 = 9/1
8 = 8/1 × 1/1 = 8/1
6 = 6/1 × 1/1 = 6/1
5 = 5/1 × 1/1 = 5/1
Answer:
Shes needs to work 26.67 hours
Step-by-step explanation:
In order to find the amount of time she needs to work, we need to divide the total by the rate that she earns money at. She needs a total of $400 and she gets 15 every hour.
400/15=26.67
Shes needs to work 26.67 hours