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ANTONII [103]
3 years ago
13

What is the value of i^n in if the remainder of n/4 is 2?

Mathematics
2 answers:
LekaFEV [45]3 years ago
5 0

The value of {i^n} is \boxed{ - 1} if the remainder of \dfrac{n}{4} is 2.

Further Explanation:

Given:

The remainder of \dfrac{n}{4} is 2.

Explanation:

The sum of imaginary numbers and real numbers is known as the complex number.

The complex number can be expressed as follows,

\boxed{z = a + ib}

Here, a is the real part of the complex number and \text{ib} is the imaginary part of the complex number.

\sqrt{ - 1} can be denoted by i.

The value of {i^2} is -1.

{i^2} =  - 1

The value {i^3} can be obtained as follows,

\begin{aligned}{i^3}&= {i^2} \times i\\&= - 1 \times i \\&= - i\\\end{aligned}

The value {i^4} can be obtained as follows,

\begin{aligned}{i^4} &= {i^2} \times {i^2}\\&= - 1 \times - 1 \\&= 1\\\end{aligned}

The value of {i^n} is \boxed{ - 1} if the remainder of \dfrac{n}{4} is 2.

Learn more:

  1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Complex numbers

Keywords: value, i^ n, remainder, n/4, 2 quotient, divisor, complex number, imaginary number, real number, exponents, dividend, powers, -1, imaginary roots.

Anastasy [175]3 years ago
5 0

i² = -1

_____

i⁰ = 1

i¹ = i

i² = -1

i³ = -i

and then the pattern repeats

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coldgirl [10]

Answer:

1. 16=v    top left

2. n=5.8   bottom left

3. n= -31.9   top right

4. b= 6 .   bottom right

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5 0
3 years ago
annalise makes rectangular patchworks quilts out of leftover fabric scraps. the first scrap she is using to make a quilt has a w
tester [92]

The area is given by f(x) = 10x² + 31x + 15.

The function is a rectangle's area function.

Rectangle Area = Length * Width

The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.

Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.

Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15

Therefore the area is given by f(x) = 10x² + 31x + 15.

Learn more about the area here -

brainly.com/question/13293720

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6 0
2 years ago
Whats x and whats y?​
andriy [413]

Answer:

Step-by-step explanation:

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4 0
3 years ago
A coin bank that excepts only nickels and dimes contains $9.15. There are three more than twice as many nickels as there are dim
valentinak56 [21]

45 dimes and 93 nickels were in bank

<em><u>Solution:</u></em>

Let "n" be the number of nickels

Let "d" be the number of dimes

We know that,

value of 1 nickel = $ 0.05

value of 1 dime = $ 0.10

<em><u>Given that There are three more than twice as many nickels as there are dimes</u></em>

Number of nickels = 3 + 2(number of dimes)

n = 3 + 2d ---- eqn 1

<em><u>Also given that coin bank that excepts only nickels and dimes contains $9.15</u></em>

number of nickels x value of 1 nickel + number of dimes x value of 1 dime = 9.15

n \times 0.05 + d \times 0.10 = 9.15

0.05n + 0.10d = 9.15  ---- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

Substitute eqn 1 in eqn 2

0.05(3 + 2d) + 0.10d = 9.15

0.15 + 0.1d + 0.10d = 9.15

0.2d = 9

<h3>d = 45</h3>

From eqn 1

n = 3 + 2(45)

n = 3 + 90 = 93

<h3>n = 93</h3>

Thus 45 dimes and 93 nickels were in bank

3 0
3 years ago
What is the quadratic equation that has roots of ,-3 And 2/5​
prohojiy [21]

Answer: 5x² + 13x - 6 = 0

Step-by-step explanation:

Represent the roots with X i.e.

X = -3 ; X = 2/5

Moving the values of X over the equator we have;

X + 3 = 0 ; 5X - 2 = 0

Equating both equations to zero we can obtain;

(X + 3)(5X - 2) = 0

Opening the brackets we get;

5x² - 2x + 15x - 6 = 0

The  result of the above equation gives;

5x² + 13x - 6 = 0

6 0
3 years ago
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