Answer:
1) multiplicative inverse of i = -i
2) Multiplicative inverse of i^2 = -1
3) Multiplicative inverse of i^3 = i
4) Multiplicative inverse of i^4 = 1
Step-by-step explanation:
We have to find multiplicative inverse of each of the following.
1) i
The multiplicative inverse is 1/i
if i is in the denominator we find their conjugate
![=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i](https://tex.z-dn.net/?f=%3D1%2Fi%20%2A%20i%2Fi%5C%5C%3Di%2Fi%5E2%5C%5C%3DWe%5C%2C%5C%2C%20know%5C%2C%5C%2C%20that%5C%2C%5C%2C%20i%5E2%20%3D%20-1%5C%5C%3Di%2F%28-1%29%5C%5C%3D%20-i)
So, multiplicative inverse of i = -i
2) i^2
The multiplicative inverse is 1/i^2
We know that i^2 = -1
1/-1 = -1
so, Multiplicative inverse of i^2 = -1
3) i^3
The multiplicative inverse is 1/i^3
We know that i^2 = -1
and i^3 = i.i^2
![1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i](https://tex.z-dn.net/?f=1%2Fi%5E3%5C%5C%3D1%2Fi.i%5E2%20%5C%5C%3D1%2Fi%28-1%29%5C%5C%3D-1%2Fi%20%2A%20i%2Fi%5C%5C%3D-i%2Fi%5E2%5C%5C%3D%20-i%2F-1%5C%5C%3D%20i)
so, Multiplicative inverse of i^3 = i
4) i^4
The multiplicative inverse is 1/i^4
We know that i^2 = -1
and i^4 = i^2.i^2
![=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1](https://tex.z-dn.net/?f=%3D1%2Fi%5E2.i%5E2%5C%5C%3D1%2F%28-1%29%28-1%29%5C%5C%3D1%2F1%5C%5C%3D1)
so, Multiplicative inverse of i^4 = 1
Answer:
4
Step-by-step explanation:
Answer:
He earned $18
Step-by-step explanation:
So what you would do is draw a calendar and put Monday, Tuesday, Wednesday, Thursday, Friday, Saturday put any random year , month ,day . You can choose any three days you want to do. After you do that put $6 for each of the three days and above put 1 hour after that you're going to multiply 6 x 3 which is $18.
Answer:
8 = r
Step-by-step explanation:
69 = 9r -3
Add 3 to each side
69+3 = 9r -3+3
72 = 9r
Divide each side by 9
72 / 9 = 9r/9
8 = r
Answer:
B
Step-by-step explanation:
There are 48 flavors and toppings. Since 16 are flavors, 32 are toppings. Dividing the 32 topping equally between 8 children is 4 toppings per child.
32 ÷ 8 = 4