What is each power of i with its multiplicative inverse.
1. i
2. i ^2
3. i ^3
4. i ^4

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

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

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

so, Multiplicative inverse of i^4 = 1

the answer is a.

135 and 80

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west