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
Solve with a system of equations: Two angles are supplementary if the sum of their measures are 180 degrees. If one is 90 degree
julsineya [31]

Answer:

  The measures of the angles are 150° and 30°.

Step-by-step explanation:

Let x and y represent the measures of the angles, with x representing the larger angle.

  x + y = 180 . . . . . . the two angles are supplementary

  x = 90 + 2y . . . . . one is 90° more than twice the other

___

Substituting the expression given by the second equation into the first, we have ...

  (90 +2y) +y = 180

  3y = 90 . . . . . . . . . . collect terms, subtract 90

  y = 30 . . . . . . . . . . . divide by the coefficient of y

  x = 180 -y = 150

The measures of the angles are 150° and 30°.

6 0
3 years ago
Find the sine ratio of angle Θ. Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no sp
Ainat [17]

Answer:

sinΘ = \frac{12}{13}

Step-by-step explanation:

sinΘ = \frac{opposite}{hypotenuse} = \frac{AB}{BC} = \frac{12}{13}

5 0
2 years ago
Jeremy will roll a number cube, numbered 1-6, twice. What is the probability of rolling an even number than the number 3?
andreyandreev [35.5K]
There are 6 possible outcomes on a dice. Meaning when you roll it it could be any of them. Because 3 is one of the 6 the answer would be 1/6
3 0
3 years ago
A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his exper
SpyIntel [72]

The population of the bacteria after 7 hours is 230 bacteria.

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population of bacteria after x hours.

Given that he starts his experiment with 200 bacteria, hence

a = 200

The bacteria grow at a rate of 2% per hour, hence:

b = 100% + 2% = 1.02

The exponential equation becomes:

y = 200(1.02)ˣ

After 7 hours:

y = 200(1.02)⁷ = 230

The population of the bacteria after 7 hours is 230 bacteria.

Find out more at: brainly.com/question/12490064

6 0
2 years ago
The price of 1 kg of silver on 1st January 2010 was $607
sveta [45]

Answer:

550

Step-by-step explanation:

9.4/100 multiplied by 607 is 57

subtract this from 607 and the answer is 549.9, to the nearest dollar is 550

5 0
3 years ago
Other questions:
  • HELP ASAP Which list is in order from least to greatest
    13·2 answers
  • Help with parentheses 100 points per answer and also brainlyest to first answer
    12·2 answers
  • Solve the equation for y (picture below)<br> Please show work and solve as much as you can
    11·1 answer
  • Jack has two more than half as many cups as
    12·1 answer
  • What is the inequality??
    11·2 answers
  • Michael graphs the equations y= -1/2+4 and y = x + 1 to solve the equation -1/2x+4= x+1. His graph is shown below. What are the
    12·1 answer
  • Melvin drinks 2 liters of water every day. There are approximately 29.6 milliliters in 1 fluid ounce. Which measurement is close
    12·1 answer
  • Help please NO LINKS!!!!!<br> special right triangles (radical answers)
    12·2 answers
  • If tan 0 = -5, find the cot 0
    13·1 answer
  • Harry has $10 in his bank account, and he adds $2 every week. based on this information, which representation best shows the rel
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!