what is the modulus of the complex number -4+3i

Answers

Answer 1

The modulus of the complex number -4+3i is 5.

Complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit,

A complex number is a number of the form a + bi, where a and b are real numbers.

The modulus (z) of a complex number x + iy is given by:

z = √(x² + y²)

The modulus of the complex number -4+3i is:

[tex]z=\sqrt{(-4)^2+3^2} =\sqrt{25}=5[/tex]

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Related Questions

Tell whether the ordered pair is a solution to the system.
(-1, -2) 3x + 5y = 3
-9x - 8y = -9
no
yes

Answers

Answer:

Step-by-step explanation:

no. substitute -1 for x and -2 for y.

the first one is -1 - 10

this equals -11 not 3

I think it’s a no but but I’m not sure

Let a and b be real numbers where ab+0. Which of the following functions could represent the graph below?
O f(x) = x(x – a)3(x – b) 3
O f(x) = (x – a)2(x – 614
O f(x) = x(x – a) (x – 5)2
O f(x) = (x – a)5(x – b)

Answers

The following functions could represent the graph below then the correct option is B; y = (x - a)^2 (x - b)^4.

What is graph ?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

we have given that a and b are real numbers different than zero.

From the graph, we can see that the line touches the x-axis in two values.

Now, if we would have an equation such as:

y = x(x - a)^3 (x - b)^3

then when x = 0

y = 0(0-a)^3 (0-b)^3

y = 0

But in the graph, we can see that when x = 0, the value of y is different than zero,

(For example, if x > a and x < b we would have a negative value for y)

Then the correct option is B ;y = (x - a)^2 (x - b)^4

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4 1/2 x 5 Multiply and answer with a mixed number in the simplest form.

Answers

Answer:

[tex]22\frac{1}{2}[/tex]

Step-by-step explanation:

(4.5)(5) = 22.5

[tex]22.5 = 22\frac{1}{2}[/tex]

How do u Keep change change this number???

1.3 - -300=????

I don’t know what to do

Answers

1 .3 - -300
1.3 + 300
301.3

The function f is given by f(x) = (x + 3)^2 - 1.
1) Write the coordinates of the vertex of the graph of f.
2) Does the graph open up or down? How do you know?

Answers

Answer:

the coordinate of the vertex is going to be (-3,-1) and it's concave up

Step-by-step explanation:

1.notice this function is in graphing form (x-h)^2+k, where (h,k) is your coordinate of the vertex, hence in this problem it's going to be (-3,-1)

2. notice that this function have a parent function of x^2, where it's a parabola that is concave up which in this case is basiclly the same shape it's also concave up

In calculus, we can proof it by finding the first derivatives and find the critical points, then take the second derivative at that critical points to see if that's negative or positive in this case it's positive

Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation: S = 5.1 + 1.5 x estimates the amount of sales ( S ) of statin in billions of dollars x years after 1998.

Answers

It would increase the days your grow

Which values of k would cause this system of equations to have no solution? Check all that apply. 6x 4y = 14, 3x 2y = k â€"2 5 7 10 21.

Answers

The values of k that will cause the system of equations to have no solution is; k = 7 and 21

We are given the simultaneous equations;

6x - 4y = 14

3x - 2y = k

Now, for both equations not to have a solution it means that x and y can't be made to be subjects.

Now, by inspection see see that the left hand side of the second equation when multiplied by 2 gives the left hand side of the first equation.

By implication, for both equations not to have a solution, k must also be multiplied by 2 to give 14.

Thus;

2k = 14

k = 14/2

k = 7

Also, since 21 is 1.5 multiplied by 14, it means that when we make 21 to be k, there will also be no solution.

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Answer:

-2, 5, 10, 21

A, B, D, E

May I please receive help?

Answers

Answer:

24°

Step-by-step explanation:

(4y-4)+(180-52)+3y = 180°

4y-4+128+3y = 180

7y+124 = 180

7y = 56

y = 8

SO ∠x = 3y

∠x = 3(8)

∠x = 24

Answer:

Step-by-step explanation:

to find the measure of angle X we must first find y

An exterior angle of a triangle is equal to the sum of the opposite interior angle

angle wyz is an exterior angle and the opposite interior angles are w and x

this means that angle wyz = angle w + angle X

if angle wyz = 52 , angle X = 3y and angle w = 4y-4 then 52 = 3y + 4y - 4

note that we just created an equation that we can use to solve for y

we now solve for y using the equation we just created

52 = 3y + 4y - 4

combine like terms

52 = 7y - 4

add 4 to both sides

56 = 7y

divide both sides by 7

we're left with y = 8

Now to find the measure of angle X we simply plug in the value of y into 3y because angle X = 3y

angle X = 3y

y = 8

angle X = 3(8)

multiply 3 and 8 to get 24

angle X = 24

and we are done!

Each week, the price of oranges at the farmer's market increases by 20%.

The price of oranges this week is $4.50.

What was the price last week?

Answers

Answer:

3.6? I don't really know

Smallest Positive fraction

Answers

Answer: 1/5?

Step-by-step explanation:

The two parallel sides of a trapezium are 19.8 and 7.2 and its area is 135 cm²..find its height

Answers

Answer:

10cm

Step-by-step explanation:

the formula for an area of a trapezium:

[tex] \frac{(a + b) \times h}{2} = area[/tex]

where a and b are the parallel sides and h is the height. equating what we have:

[tex] \frac{(19.8 + 7.2) \times h}{2} = 135[/tex]

simplify the numerator by adding 19.8 and 7.2=27

[tex] \frac{27h}{2} = 135[/tex]

multiply both sides by 2

[tex]27h = 270[/tex]

divide both sides by 27

[tex]h = \frac{270}{27} = 10[/tex]

the height is 10cm

When the swimming pool is 25% full, it takes 2250 cubic meters (m3) to fill it up from that point. When it is full, it can be emptied at a rate of 120 m3/h. How many hours does it take to empty an 80% full pool?

Answers

Answer:

20 hours

Step-by-step explanation:

The volume of water when the pool is 80% full can be found using the proportion ...

2250/75% = v/80%

v = (80/75)(2250) = 2400 . . . cubic meters

Emptying at the rate of 120 m³/h will take ...

time = volume/rate

time = (2400 m³)/(120 m³/h) = 20 h

It will take 20 hours to empty the pool from 80% full.

I think of a number, increase it by four and double the answer. The
result is 20 more than the number. Find this number.

Answers

Answer:

(x+4)2=x+20

2x+8=x+20

2x-x=20-8

x=12

The number I thought of is 12.

How to convert statements into numerical expressions ?

To convert statements into numerical expression break the statement into chunks write the terms with mathematical operations.Interpret twice, thrice, half of this etc logically.Practice a lot.

According to the given question I think of a number,Let the number be x.

I increase it by four and double (x+4)×2 = 2(x+4).

The result is 20 more than the number which is (x+20).

∴ 2(x+4) = (x+20)

2x + 8 = x + 20.

2x - x = 20 - 8.

x = 12.

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14. The number of customers that a small
restaurant serves increases by 25% each
week. The restaurant served 400 customers
the first week it was open.
How many customers did the restaurant
serve during the third week?

Answers

Answer:

625

Step-by-step explanation:

ok so, 25% of 400 is 100 since 25 is 1/4 of 100 just like 100/400. Now, we do 100+ 400 for the second week which is 500. Now, 500 divided by 25 is next and if we had 4 boxes wed be able to fit 100 in each and the last 100 is split so 100 divided by 4 is 25. so we add 25 to each box. Now we have 125 in each box. so thats it divided by 25% or 1/4. 125 + 500 is 625 and thats your awnser. Have a good day!

Jenna has 38 coins. She uses 19 coins to buy a notebook. How many coins does she have left?
Explain how you can solve and check this problem.

Answers

Answer: 19 coins

Step-by-step explanation:

38-19=19

To check, take any one of the nubers and replace it with x, and when you solve for x. you'll get that number back. For example:

Let x represent the amount used to buy a notebook

19+x=38

x=38-19

x=19

38 coins - 19 coins = 19 coins

You solve the problem by subtracting how many coins she used by how many coins she has

1+1=3 proof
needs step by step explanation

Answers

Answer:

1+1=3, See explenation

Step-by-step explanation:

1+1=2 but thats basically 2.1 because whole numbers are boring, but 2.1 is basically 2.2 because we want it as an even number, but 2.2 is basically 2.3 because 2.3 is the luckiest number, which is basically 2.5 if you think about it because 2.3 looks like 2/3 and two thirds can't be a whole (which is why we say 3/3 instead of 2/3) and 2.5 rounded up is 3. So thats how 1+1=3

Please help me with this math problem!! NO LINKS PLEASE!! IT'S DUE TONGIHT AT 11:59PM!! :)

Answers

Answer:

∆L = 51°

∆Y = 28°

∆B = 101°

∆U = 51°

UG = 10.66666

BG = 4x

Write the gcf of:
200x^2y^5 and 1000x^3y^2

Answers

Answer:

Step-by-step explanation:

200 divides into 1000 so that is part of the HCF.

x^2 and x^3 are present so the HCF contains x^2

y^2 and y^5 are present so the HCF contains y^2

HCF = 200*x^2 * y^2

What is the solution set for x^2 - 2x - 15 = 0

A. {-5, -3}

B. {5, -3}

C. {3, 5}

D. {-3, 5}

Answers

Answer:

Step-by-step explanation:

I have done this before

PLEASE SHOW ALL WORK AND DO CORRECTLY

For #8 , fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.

8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2

Answers

Answer:

26.2 cm

Step-by-step explanation:

Area = (b1 + b2)/2 * h

401.92 = (x + 14.4)/2 * 19.8

Divide each side by 19.8

20.2989 = (x + 14.4)/2

Multiply each side by 2

40.6 = x + 14.4

Subtract 14.4 from each side

x = 26.2

Answer:

116.82

Step-by-step explanation:

Since your trying to find a missing base

19.8 x 14.4= 285.12

401.94-285.12=116.82

Hopes This Helps

if 240 slices of cake are shared into the same ration 3:5 among the boys and girls how many slices will each students recieve

Answers

7 slices each your welcome r

how do I do this question?

Answers

Answer:

x = (y +2)/3

Step-by-step explanation:

y= 3x-2

y+2=3x

x=(y +2)/3

Select all the intervals where f is increasing.

A. −3 < x < −2
B. -1.5 < x < 0
C. 3.5 < x < 4.5
D. None of the above

Answers

Step-by-step explanation:

since f(x) is overall increasing for the interval -3 < x < 0,

A and B both fit in there and are correct answers.

Answer:

C. 3.5 < x < 4.5

Step-by-step explanation:

Anything that is above 1 (4, 9, etc) is increasing and anything that is below 1 (0.4, -3, etc) is decreasing. A and B are wrong because they are negative or below 1 and it isn't D because C is increasing.

Given g(r) = 3 – 8r, find g (–3).

Answers

Answer: R = 3/5

Step-by-step explanation:

i think

How do I solve this?

Answers

C) 18 minutes
This is because each sparkler takes 2 minutes to burn so 10 * 120 = 1200 seconds, then 120 / 0.10 = 12 (which is the 10th of the 2 minutes) now we do 12 * 10 = 120 to get the cut time from lighting a match after a tenth remained. now since we have that we do 1200 - 120 and get 1080 seconds and that is the total time n seconds of the burning matches, now we convert it to minutes by doing 1080 / 60 and get 18.
hope this is helpful!

the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.

Answers

The pattern in the given series of amount in the account are in the form of

arithmetic and geometric progression.

The function for Option 1 is; [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]The function for Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]

Reasons:

The given table of values is presented as follows;

[tex]\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right][/tex]

In Option 1, the amount in dollars for each year has a common difference of d = 100

The first term, a = 1,100

Therefore;

The Option 1 can be represented as an arithmetic progression , A.P. in the

form, tₙ = a + (n - 1)·d as follows;

For the Option 1, we have;

The amount in dollars after n years, [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]

For Option 2, it is possible to find;

1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1

Therefore;

The terms in the Option 2 have a common ratio of r = 1.1

The Option 2 is a geometric progression, G.P.

The first term in Option 2 is a = 1,100

Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾

Therefor;

The function for the Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]

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468 divided by 3 step by step solution

Answers

Answer:

156

Step-by-step explanation:

468 ÷ 3

= 156

hope u liked the answer :)

#keep learning

I need help on this question. please help me.. I don't have idea on this.

Answers

Answer:

Step-by-step explanation:

5(-4 +10) × 4.8 ÷ [tex]\frac{3}{4}[/tex]

5(6) × 4.8 ÷ [tex]\frac{3}{4}[/tex]

30 × 4.8 ÷ [tex]\frac{3}{4}[/tex]

30 × 4.8 × [tex]\frac{4}{3}[/tex]

_________________________________

Hope this helps!!

If I have made a mistake, please let me know; I enjoy leaning from them:)

Answer:

Step-by-step explanation:

Can i get some help :

Answers

The store owner is adding cost, so we will use addition. The answers should be as follows:

[] c + $3.49 = $9.84

[] c = $6.35 <- subtract $3.49 from both sides of the equation

[] Solution of answer represents the old cost of the toy.

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

What is the end behavior of the function shown in the graph above?
A
As x approaches 0, y approaches 15.
As x approaches 25, y approaches 0.

B
As x approaches∞, y approaches 0.
As x approaches −∞, y approaches ∞.

C
As x approaches 0, y approaches ∞.
As x approaches ∞, y approaches −∞.

D
As x approaches ∞, y approaches 0.
As x approaches ∞, y approaches ∞.

Answers

Answer:

Step-by-step explanation:

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