Answer:
![(2-5i)(p+q)(i)=29i](https://tex.z-dn.net/?f=%282-5i%29%28p%2Bq%29%28i%29%3D29i)
Step-by-step explanation:
We have the product of 2 complex numbers
![(2-5i)(p+q)(i)](https://tex.z-dn.net/?f=%282-5i%29%28p%2Bq%29%28i%29)
We know that:
![p=2\\\\q=5i](https://tex.z-dn.net/?f=p%3D2%5C%5C%5C%5Cq%3D5i)
Then we substitute these values in the expression
![(2-5i)((2)+(5i))(i)](https://tex.z-dn.net/?f=%282-5i%29%28%282%29%2B%285i%29%29%28i%29)
![(2-5i)(2+5i)(i)](https://tex.z-dn.net/?f=%282-5i%29%282%2B5i%29%28i%29)
The product of a complex number
by its conjugate
is always equal to:
![a ^ 2 - (bi) ^ 2](https://tex.z-dn.net/?f=a%20%5E%202%20-%20%28bi%29%20%5E%202)
Then
![(2-5i)(2+5i)(i)=(2^2-5^2i^2)(i)](https://tex.z-dn.net/?f=%282-5i%29%282%2B5i%29%28i%29%3D%282%5E2-5%5E2i%5E2%29%28i%29)
Remember that:
![i=\sqrt{-1}\\\\i^2 = -1](https://tex.z-dn.net/?f=i%3D%5Csqrt%7B-1%7D%5C%5C%5C%5Ci%5E2%20%3D%20-1)
So
![(2^2-5^2i^2)(i)= (4 - 25(-1))(i)\\\\(4 - 25(-1))(i) = (4+25)i=29i](https://tex.z-dn.net/?f=%282%5E2-5%5E2i%5E2%29%28i%29%3D%20%284%20-%2025%28-1%29%29%28i%29%5C%5C%5C%5C%284%20-%2025%28-1%29%29%28i%29%20%3D%20%284%2B25%29i%3D29i)
Finally
![(2-5i)(p+q)(i)=29i](https://tex.z-dn.net/?f=%282-5i%29%28p%2Bq%29%28i%29%3D29i)
Answer: x = 2
Step-by-step explanation:
You need to subtract the 9from both sides to cancel out the 9 on the side of the x
Then you divide -18/-9 and you get +2
Member two negative numbers divided make a postitive
Answer:
g = 4
Step-by-step explanation:
5g = 20
Divide each side by 5
5g/5 = 20/5
g = 4
Answer:
432 people on Friday and 658 on Saturday
Step-by-step explanation:
Lets use variables for each day
x=Friday and y=Saturday
now write two equations since you were given two different information (money and people)
$6 on Friday and $8 on Saturday with a total amount of $7856
the equation will be 6x+8y=7856
now the second equation will be for people
x amount of people on Friday and y amount of people on saturday for a total of 1090; the equation will be
x+y=1090
put them together
6x+8y=7856
x+y=1090
now you can cancel a variable but manipulating one of the equations. We'll use x, to cancel x you need make it zero so multiply the bottom by -6
6x+8y=7856
-6(x+y=1090)
6x+8y=7856 now subtract downwards, with the x cancelling
-6x-6y=-6540
2y=1316 simplify
(2y/2)=(1316/2)
y=658
insert y into x+y=1090
x+(658)=1090
-658 -658
x=432