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3 years ago

What is the best method to geometrically show the addition of complex numbers?

Mathematics

1 answer:

Jlenok [28]3 years ago

8 0

Answer:

Multiplying a complex number by a real number

Explanation:

For example, 2 times 3 + i is just 6 + 2i. Geometrically, when you double a complex number, just double the distance from the origin, 0. Similarly, when you multiply a complex number z by 1/2, the result will be half way between 0 and z.

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Underline all the ordered pairs (x,y) that are solutions to the equation y=2x+1.

Romashka [77]

Answer:

(3,7) (7,3) (−1,14) (0,1) (12,25)

(5,11) (0,12) (1,8) (12,0) (−1,−1)

Step-by-step explanation:

We have the following function:

$y = 2x+1$ .

We are going to check if each ordered pair is a solution.

(3,7)

If when $x = 3, y = 7$ , it is a solution.

$y = 2x + 1 = 2(3) + 1 = 7$

This ordered pair is a solution.

(7,3)

If when $x = 7, y = 3$ , it is a solution.

$y = 2x + 1 = 2(7) + 1 = 15$

This ordered pair is not a solution.

(-1,14)

If when $x = -1, y = 14$ , it is a solution.

$y = 2x + 1 = 2(-1) + 1 = -1$

This ordered pair is not a solution.

(0,1)

If when $x = 0, y = 1$ , it is a solution.

$y = 2x + 1 = 2(0) + 1 = 1$

This ordered pair is a solution.

(12,25)

If when $x = 12, y = 25$ , it is a solution.

$y = 2x + 1 = 2(12) + 1 = 25$

This ordered pair is a solution.

(5,11)

If when $x = 5, y = 11$ , it is a solution.

$y = 2x + 1 = 2(5) + 1 = 11$

This ordered pair is a solution.

(0,12)

If when $x = 0, y = 12$ , it is a solution.

$y = 2x + 1 = 2(0) + 1 = 1$

This ordered pair is not a solution.

(1,8)

If when $x = 1, y = 8$ , it is a solution.

$y = 2x + 1 = 2(1) + 1 = 3$

This ordered pair is not a solution.

(12,0)

If when $x = 12, y = 0$ , it is a solution.

$y = 2x + 1 = 2(12) + 1 = 25$

This ordered pair is not a solution.

(-1,-1)

If when $x = -1, y = -1$ , it is a solution.

$y = 2x + 1 = 2(-1) + 1 = -1$

This ordered pair is a solution.

3 0

3 years ago

5. LETTERS How many ways can you arrange the letters in the word history?

SIZIF [17.4K]

Answer:

5040

Step-by-step explanation:

You get this number by using the mathematical process of factorials.

Since history has seven words, we will solve seven factorial.

7! = 5040

3 0

3 years ago

Read 2 more answers

If DEF measures 32 inches, EF = 2x - 10 and DE= 4x find x and the measure of each segment.

azamat

Add EF and DE together to equal 32

2x-10 + 4x = 32

Combine like terms;

6x-10 = 32

Add 10 to each side:

6x = 42

Divide both sides by 6:

x = 42/6

X = 7

EF = 2x-10 = 2(7)-10 = 14-10 = 4

DE = 4x = 4(7) = 28

5 0

3 years ago

consider the gre scores for a random sample of 6 students out of a class of 25: name julia andrew jason cathy jessica robert sco

Thepotemich [5.8K]

Name Score
Julia 650
Andrew 550
Jason 380
Cathy 720
Jessica 710
Robert 550

Point estimate for the mean score:
Sample mean = sum of all observations / number of observations

sample mean = (650+550+380+720+710+550) / 6
sample mean = 3560 / 6
sample mean = 593.33

The point estimate for the mean score is 593.33

6 0

3 years ago

2³+2²+2÷2²+2+1=2 prove that this relation is true for any natural numbers

UkoKoshka [18]

So, this question is basically asking us "If we had an x instead of a 2, would this be true?" We can try and see what we get:

$\frac{x^3+x^2+x}{x^2+x+1}=x$

So, if we want to show this we have to change the numerator or denominator in such a way that we can cancel some common factors. Notice that $x^3+x^2+x=x(x^2+x+1)$

If we replace the factored numerator with the original one, we get:

$\frac{x(x^2+x+1)}{x^2+x+1}=x \implies \\ x=x$

Since we have an equality, this relation is proved.

3 0

3 years ago