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
Juliette [100K]
2 years ago
5

Using De-Moivre's theorem, prove that i^2= -1.​

Mathematics
1 answer:
Novosadov [1.4K]2 years ago
3 0

Write i in trigonometric form. Since |i| = 1 and arg(i) = π/2, we have

i = exp(i π/2) = cos(π/2) + i sin(π/2)

By DeMoivre's theorem,

i² = exp(i π/2)² = exp(i π) = cos(π) + i sin(π)

and it follows that i² = -1 since cos(π) = -1 and sin(π) = 0.

You might be interested in
Solve for a.<br><br> 5a - 2 = 23
Sphinxa [80]
The answer to the question is 5
5 0
2 years ago
Read 2 more answers
Hurrrryyyyy plllzzz. Determine the equation of the line that passes through the given points
pashok25 [27]
<h2>Answer:</h2>

y = 2

<h2>Step-by-step explanation:</h2>

To determine the equation of the line that passes through (10,2) and (-3,2), we need to determine the slope of the line. Then substitute the slope and any given point in point slope form to obtain the equation of the line.

<h3>Finding the Slope of the line:</h3>

\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1}  }

\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1}  }

<u>Substitute the coordinates of the given points:</u>

\implies \text{Slope} = \dfrac{2 - 2}{-3 - 10  }

<u>Simplify the equation to determine the slope:</u>

\implies \text{Slope} = \dfrac{0}{-3 - 10  }

∴ 0 divided by ANY number is ALWAYS 0.

\implies \text{Slope} =0

<h3>Finding the equation of the line:</h3>

Point slope form formula: y - y₁ = m(x - x₁)

  • x₁ and y₁ are the coordinates of any given point.
  • m is the slope

<u>Substitute the values in the point slope form:</u>

\implies \text{Equation of line:} \ y - y_{1}  = m(x - x_{1} )

\implies \text{Equation of line:} \ y - 2  = 0(x - 10)

<u>Simplify the equation to determine the equation of the line:</u>

∴ Any number multiplied by 0 is 0.

\implies \text{Equation of line:} \ y - 2  = 0

\implies \text{Equation of line:} \ y   = 0 + 2

\implies \text{Equation of line:} \ y   = 2

Thus, the equation of the line is y = 2.

5 0
2 years ago
JoAnn is taking a trip to visit her family. After one day of driving, she has traveled 315.2 miles. If JoAnn lives 510 miles fro
Elena L [17]

Answer:

194.8 miles

Step-by-step explanation:

510 - 315.2 = 194.8

Hope this helps!

8 0
3 years ago
Read 2 more answers
Company A: $21 per jersey<br>company B: $18 per jersey+$45 fee. when is company a best?
Anni [7]
So I would first find out when they are equal then do one more than that. 21x=18x+45, 3x=45, x=15 so the answer would be 16 jerseys
7 0
3 years ago
You start driving north for 16 miles, turn right, and drive east for another 30 miles. At the end of driving, what is your strai
Maru [420]

The distance between starting and ending point is 34 miles.

Step-by-step explanation:

Given,

Car moves 16 miles to north then 30 mile to east.

It forms a right angle triangle.

The straight line distance from starting to ending point represents hypotenuse.

To find the distance between starting and ending point.

Formula

By <em>Pythagoras theorem,</em>

h² = b²+l² where h is the hypotenuse, b is base and l is the another side.

Taking, b=16 and l=30 we get,

h² = 16²+30²

or, h = \sqrt{256+900}

or, h = \sqrt{1156} = 34

Hence,

The distance between starting and ending point is 34 miles.

5 0
3 years ago
Other questions:
  • A linear regression equation of the best fit between a students attendance and the degree of success in school is h =. 0.5x + 68
    6·1 answer
  • This is the question​
    5·2 answers
  • What is the answer to this math problem? 6=a/4+2
    7·1 answer
  • The function h(x) = 2.5x + 20 represents your height in inches, h(x), for x years you have been alive. How many inches tall will
    12·1 answer
  • 192.5=1/2(26+12.5)h. What is the unknown measure
    7·1 answer
  • What is the answer to 50-43+(6x8)-9+3 and how do you solve it?
    10·2 answers
  • PLS HELP Will give brainliest
    14·1 answer
  • Pls help thanks in advance
    11·1 answer
  • Please answer quickly Thank You
    13·1 answer
  • Jasmin rakes at two different houses. It takes her 2 1/3 hours to rake leaves at the first. It takes her 1/2 of that time to rak
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!