Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
![14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right]](https://tex.z-dn.net/?f=14%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%20%5C%3A%7D%7B5%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%20%5C%3A%5C%3A%7D%7B5%7D%5Cright%29%5Cright%5D%5Ccdot%20%5C%3A2%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B3%5Cpi%20%5C%3A%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B3%5Cpi%20%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%5Cright%5D)
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = 
,
sin(π / 5) = 
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
![14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right]](https://tex.z-dn.net/?f=14%5Cleft%5B%5Cfrac%7B%5Csqrt%7B5%7D%2B1%7D%7B4%7D%2Bi%5Cfrac%7B%5Csqrt%7B2%7D%5Csqrt%7B5-%5Csqrt%7B5%7D%7D%7D%7B4%7D%5Cright%5D%5Ccdot%20%5C%3A2%5Csqrt%7B2%7D%5Cleft%5B0-i%5Cright%5D)
And now simplify the expression,
The exact value of 
= 
and 
= 
Therefore we have the expression 
, which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = 
,
sin(π / 3) = 
,
cos(- π / 6) = ,
sin(- π / 6) = 
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
![15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right]](https://tex.z-dn.net/?f=15%5Cleft%5Bcos%5Cleft%28%5Cfrac%7B%5Cpi%20%5C%3A%7D%7B3%7D%5Cright%29%2Bisin%5Cleft%28%5Cfrac%7B%5Cpi%20%5C%3A%5C%3A%7D%7B3%7D%5Cright%29%5Cright%5D%20%5Cdiv%20%5C%3A3%5Csqrt%7B2%7D%5Cleft%5Bcos%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%7D%7B6%7D%5Cright%29%2Bisin%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%7D%7B6%7D%5Cright%29%5Cright%5D)
⇒
![15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right]](https://tex.z-dn.net/?f=15%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright%5D%5Cdiv%20%20%5C%3A3%5Csqrt%7B2%7D%5Cleft%5B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2B-%5Cfrac%7B1%7D%7B2%7D%5Cright%5D)
The simplified expression will be the following,
or in other words 
or 
The solution will be option a, as you can see.
Answer:
p=-6
Step-by-step explanation:
14 = -(p-8) (distribute negative into parentheses)
14 = p(-1) -8(-1)
14 = -p + 8 (subtract 8 from both sides)
14 - 8 = -p
6 = -p (multiply both sides by -1 and rearrange)
p = 6(-1) = -6
Answer:
The red line has a slope of -1
Step-by-step explanation:
This is because parallel lines have the same slope with a different y intercept.
If the green line's slope is -1 and it is parallel to the redline, they will have the same slope.
Answer:
Both of them would just stay how they are
Step-by-step explanation:
Unless the x and y have a value that you have shown it would just stay at the same standard so there is not answer also no answer would be added.
Answer:
Hypotenuse = 10 Cm
Step-by-step explanation:
Given:
θ = 60°
Base = 5 cm
Hypotenuse = x cm
Find:
Hypotenuse
Computation:
Cos θ = Base / Hypotenuse
Cos 60° = 5 / Hypotenuse
0.5 = 5 / Hypotenuse
Hypotenuse = 10 Cm
