1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
hammer [34]
3 years ago
9

What is each power of i with its multiplicative inverse.

Mathematics
1 answer:
pentagon [3]3 years ago
3 0

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

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

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

so, Multiplicative inverse of i^4 = 1

You might be interested in
How do I multiply this mixed fraction?
valentinak56 [21]
Change the fraction into a decimal
3 0
3 years ago
Read 2 more answers
The ratio of Victors money to Susies money is 4:7 at first. After Victor spent half of his money and Susie spent $60, Susie had
valkas [14]

Answer:

Victor originally had $80

Step-by-step explanation:

Let Victor have $4x

Let Susie have $7x

Since Victor spent half his money, he now has $2x

Susie spent $60 and thus now has $(7x - 60)

The final ratio of Victor's money to Susie's money is therefore  2x : $(7x - 60). This is given 1:2. Now we just need to solve the proportion by cross-multiplying

2x : (7x - 60) = 1:2

1 × (7x - 60) = 2 × 2x

7x - 60 = 4x

3x = 60

x = 20

Therefore Victor originally had $4x = $80.

7 0
2 years ago
Read 2 more answers
A bag of marbles contains 3 yellow, 2 red, 2 green, and 1 blue marble. What is the probability of selecting a green marble?
Papessa [141]

Answer:

2/8

Step-by-step explanation:

There are 2 green marbles.

In all, there are 8 marbles.

So, the probability is 2/8.

6 0
3 years ago
Read 2 more answers
Complete the statement. Round to the nearest hundredth if necessary. 48 ft =_____yd​
TiliK225 [7]

Answer: 16

Step-by-step explanation:

there are 3 feet in one yard so divided 48 by 3 and you get 16

8 0
2 years ago
Read 2 more answers
Find the measure of the angle to the nearest tenth of a degree.
Digiron [165]

Answer:

Option B is correct.

Step-by-step explanation:

We need to find the value of S in cos S = 0.9092

cos S = 0.9092

To find value of S we will find cos^-1(0.9092) i.e

S = cos^-1 (0.9092)

S = 24.6 °

So, the measure of the angle to the nearest tenth of a degree of cos S = 0.9092 is 24.6°

So, Option B is correct.

8 0
3 years ago
Other questions:
  • What is 7/44 in lowest terms
    11·2 answers
  • Draw a number line to<br><br> represent the inequality.<br><br> y s 23
    6·1 answer
  • Find the distance between (8,0) and (4,-4)
    5·1 answer
  • Look at this shape:which image shows a translation?
    10·1 answer
  • For each part, use the Distributive Property to write an equivalent expression
    12·2 answers
  • I need help, it’s geometry:
    15·1 answer
  • Please help me i love u so much
    12·1 answer
  • Find the distance between the points.<br><br> (9.7, -2.1), (-3.2, 8.1)
    11·1 answer
  • Simplify expression -3√2+ 3√8
    12·2 answers
  • Will give brainliest
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!