Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
Every complex number has both a real part and an imaginary part.​

Determine Whether The Following Statement Is Always, Sometimes, Or Never True. Explain Your Reasoning.

Answers

Answer 1
Number on both sides
Answer 2

The statement "Every complex number has both a real part and an imaginary part" is always true.

Every complex number is defined as a number of the form "a + bi," where "a" represents the real part and "bi" represents the imaginary part.

The real part "a" is a real number, and the imaginary part "bi" is a multiple of the imaginary unit "i," where "i" is defined as the square root of -1.

Even if a complex number has a zero imaginary part, it is still considered to have both a real and an imaginary part.

In that case, "a" represents the real part, and the imaginary part "bi" becomes zero.

For example, the complex number 3 + 0i is a real number (3) and can be represented as having a real part of 3 and an imaginary part of 0i.

In conclusion, every complex number by definition consists of both a real and an imaginary part, making the statement "Every complex number has both a real part and an imaginary part" always true.

To learn more about the complex number;

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Related Questions

Quick I need an answer PLEASE!! What is 18,931 ÷83

Answers

Answer:

228.08433734939759036144578313253.....

A flash disk has the capacity of storing 1 megabyte of data. How many kilobytes of data can be stored in the same flash disk​

Answers

For this sort of problem, you need to be familiar with prefixes.

So:

megabyte = [tex]1 *10^6[/tex] bytes

kilobyte = [tex]1*10^3[/tex] bytes

and a regular byte would just be [tex]1[/tex]

Now, you will need to do a conversion:

[tex]1megabyte*\frac{1*10^6bytes}{1megabyte}*\frac{1*10^{-3}kilobyte}{1byte}[/tex]

I'm going to explain this just in case, but we convert megabytes to regular bytes in the first half by using the information I gave you above. (In one megabyte, there are [tex]1*10^6[/tex] bytes!)

In the second fraction thought, remember one kilobyte is [tex]1*10^3[/tex] bytes. However, you usually only see one of each thing on the bottom of fractions, so you need to add a negative sign to the 3. (technically you could just do [tex]\frac{1kilobyte}{1*10^3bytes}[/tex], but I think it is more correct to do write it out how I did).

*** They do equal the same thing though! Do whichever way is easier for you!

Now, your answer should be:

[tex]10^3[/tex] kilobytes (1000 kilobytes)

Hope this helped!

Mike is planting flowers in plastic cups for his science fair project. Each of the cups is filled to the top with a mixture of soil, fertilizer, mulch, and sand in different proportions. Each cup contains 1/2 cup of soil, 1/3 cup of fertilizer, and 1/8 cup of mulch. How much sand should he use to fill the cup?

PLZ HURRY

Answers

Answer:

He will need 1/8 of sand to fill the cup

Step-by-step explanation:

For 1/2 i filled half of the cup for 1/3 i made new cup split it in 3 and added it in main cup then for 1/8 made a new cup split it in 8 and added it to main cup the test is sand.

Can you solve this equation with work? I can't figure out how to show my work for this one.

2(y+x+14) = 14 + 2x

Answers

2(y + x + 14) = 14 + 2x  

2(y) + 2(x) + 2(14) = 14 + 2x

2y + 2x + 28 = 14 + 2x

2y + 2x - 2x = 14 - 28

2y = -14

2y / 2 = -14 / 2

y = -7

Gerard collects coins. he has 103 pages of quarters in his coin collection books. each page contains 16 quarters. How many quarters does Gerard have altogether?

please help!​

Answers

Gerard has 1,648 coins in total because if one page has 16 multiply it by 103 and that’s what you get please mark me brainliest
1,648 quarters!
In order to figure this out you must multiple the number of quarters on each page which is 16 by the number of pages which is 103 & it gives you your answer!

Find the Distance rounded to a whole number.
Give the distance between (2,1) and (5,2)

Answers

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

The distance between two points can be found using the Pythagorean Theorem [tex]a^{2} + b^{2} = c^{2}[/tex].

This is because, if you connected your two points with a line, that line could be defined as the hypotenuse of a right triangle. the base of that triange is the distance between the x coordinates ([tex]x_{2} -x_{1}[/tex]) and the height by the distance between the y coordinates ([tex]y_{2} - y_{1}[/tex]). Sine these are the sides of the right triangle, they are equal to a and b above (c is the hypotenuse that we are trying to find). So, we calculate the two distances above and get 3 and 1 (for x and y respectively). 3^2 + 1^ 2 =10. So the answer is square root 10.

If a=7 and b=2 what is 2a+3b ?

Answers

Answer:

20

Step-by-step explanation:

You basically just plug in the numbers given for the variables and solve.

2(7)+3(2) = 14+6= 20

You substitute 7 in for a and 2 in for b.

−4 + 20 > −8 what the answers

Answers

Answer: -20

Step-by-step explanation: plz mark me brainliest please?

√45 * √96
Please show your work on how you got the answer!

Answers

Answer:

45=6.7, 96=9.79

Step-by-step explanation:

because (6.7)6.7 =45 that’s how square root works… squared means two times a number

what is 47+50- __ - 32

Answers

This question doesn't make sense.Are you sure you wrote it correctly?

List at least 4 common variable expenses someone might have each month.

Answers

Answer:

water, food, toliet paper, toothpaste

Step-by-step explanation:

only answer 9 or 11 or both please I want to sleep :(

Answers

Answer:

9 11

But are you okay? It spells 9-1-1.

Please Help!! I really need it!​

Answers

Answer:

1. 2:1

2. 1:2

3. 2:1:3

4. 11:4

5. 2:1

Answer:

Step-by-step explanation:

1) Apples :  Mangoes = 20 : 10  = 2 :1

2) Ponkans : Guavas = 15 : 30 = 1 : 2

3) Apples :  Mangoes : Guavas = 20 : 10 : 30: = 2 : 1 : 3

4) All  fruits = apples + mangoes + ponkans + guavas  = 20 + 10 + 15 + 30 = 75

All fruits : Apples = 75 : 20 = 15 : 4

4) apples + guavas = 20 + 30 = 40

Mangoes + Ponkans = 10 + 15 = 25

apples + guavas : mangoes + Ponkans = 40 : 25 = 8 : 5

Which expression is equivalent?

Answers

3x - 4 + (6/x) → Option A

Step-by-step explanation:

[tex]\begin{aligned}\frac{9x^2-12x+18}{3x}&=\frac{\cancel{3}\left(3x^2-4x+6\right)}{\cancel{3}x}\\&=\frac{3x^2-4x+6}{x}\\&=\frac{3x^2}{x}-\frac{4x}{x}+\frac{6}{x}\\&=\underline{\underline{\boxed{3x-4+\frac{6}{x}}}}\end{aligned}[/tex]

TRI=ANG GN= HELP ME with this

Answers

Answer:

Sup bro your answer is 17

Which statement best explains the relationship
between lines FG and HJ?
O They are perpendicular because their slopes are
equal.
• They are perpendicular because their slopes are
negative reciprocals.
They are not perpendicular because their slopes are
equal.
O They are not perpendicular because their slopes are
not negative reciprocals.

Answers

Answer:

The answer is A

Step-by-step explanation:

Use the probability distribution to complete parts (a) and (b) below.
The number of school-related extracurricular activities per student
Activities 0 1 2 3 4 5 6 7
Probability 0.059 0.121 0.164 0.179 0.212 0.127 0.086 0.052
(a) Find the mean, variance, and standard deviation of the probability distribution.
The mean is 3.3
(Round to one decimal place as needed.)
The variance is
(Round to one decimal place as needed.)

Answers

this could take a while to think about but uhh i dont know,

The variance of the probability distribution is 3.4.

To find the variance of the probability distribution, calculate the following:

1. The squared deviation of each activity value from the mean.

2. The product of each squared deviation and its corresponding probability.

3. The sum of these products.

1. Calculate the squared deviation of each activity value from the mean (3.3):

[tex]\[ (0 - 3.3)^2 = 3.3^2 = 10.89 \]\\[/tex]

[tex]\[ (1 - 3.3)^2 = (-2.3)^2 = 5.29 \][/tex]

[tex]\[ (2 - 3.3)^2 = (-1.3)^2 = 1.69 \][/tex]

[tex]\[ (3 - 3.3)^2 = (-0.3)^2 = 0.09 \][/tex]

[tex]\[ (4 - 3.3)^2 = (0.7)^2 = 0.49 \][/tex]

[tex]\[ (5 - 3.3)^2 = (1.7)^2 = 2.89 \][/tex]

[tex]\[ (6 - 3.3)^2 = (2.7)^2 = 7.29 \][/tex]

[tex]\[ (7 - 3.3)^2 = (3.7)^2 = 13.69 \][/tex]

2. the product of each squared deviation and its corresponding probability:

[tex]\[ 0.059 \times 10.89 = 0.64351 \][/tex]

[tex]\[ 0.121 \times 5.29 = 0.63909 \][/tex]

[tex]\[ 0.164 \times 1.69 = 0.27716 \][/tex]

[tex]\[ 0.179 \times 0.09 = 0.01611 \][/tex]

[tex]\[ 0.212 \times 0.49 = 0.10388 \][/tex]

[tex]\[ 0.127 \times 2.89 = 0.36703 \][/tex]

[tex]\[ 0.086 \times 7.29 = 0.62814 \][/tex]

[tex]\[ 0.052 \times 13.69 = 0.71188 \][/tex]

3. Sum up these products to get the variance:

[tex]\[ \text{Variance} = 0.64351 + 0.63909 + 0.27716 + 0.01611 + 0.10388 + 0.36703 + 0.62814 + 0.71188[/tex]

              = [tex]3.38680 \][/tex]

              =3.4

So, the variance is 3.4.

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write a number in standard form where 7 is in the tenths place

Answers

Answer:

30.75

Step-by-step explanation:

Hope this helps!

123.7 hope this helps!

What do you call raising a base to the exponent 2?

Answers

Answer:

When exponents are raised to another exponent, the exponents are multiplied. (a m) n = a (m × n) EX: (2 2) 4 = 4 4 = 256 (2 2) 4 = 2 (2 × 4) = 2 8 = 256

Step-by-step explanation:

I will brainlist who can answer this 3 Questions!​

Answers

Answer: 20. A 21. C 22. B

Step-by-step explanation: image attached below for explanation

Consider 2 3/4 divided by 1/8

(A) write a real world problem for the division

(B) create and explain a model for the division

(C) find the quotient show your work or explain your reasoning

Answers

Answer:

Part A. Mary has 2 3/4 cups of sugar to make cookies. The recipe requires 1/8 cup of sugar for one portion of cookies. How many portions of cookies can Mary make?

Part B.

 portions.

Part C. The quotient is 22 and this number represents the amount of portions of cookies that Mary can make.

Step-by-step explanation:

What is 9 - 2 to the power 2 to the power of 4 / 4 + 3 to the power of 5

Answers

Answer:

what is 3x to the power of 2 ×4x to the power of 5

Rewrite y - 3 = -9(x - 1) in standard form.

Answers

Answer:

9x + y = 12

Step-by-step explanation:

Hi there!

We are given the equation y - 3 = -9(x-1) and we want to write it in standard form

The equation is currently in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where [tex](x_1 , y_1)[/tex] is a point and m is the slope. Standard form is ax + by = c, where a, b, and c are free integer coefficients

We can first convert the equation from point-slope form into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We can distribute 9 to every term on the right side:

y - 3 = -9x + 9

Now add 3 to both sides

y = -9x + 12

Now the equation is in slope-intercept form (y=mx+b). To make it standard form, add 9x to both sides, to make the form ax + by = c .

9x + y = 12

Hope this helps!

Help, somebodyyyyyy aaaaa I need an explanation :<

Answers

Answer:

Step-by-step explanation:

wht grade is this?

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel? Write an inequality expression that represents the situation and solve! Explain your reasoning! You can copy/paste the needed symbols as needed: ≥ ≤

Answers

Answer:

The inequality expression would be 1.75+0.65x ≥10

She would be able to ride ~12.7 miles or just 12 miles rounding down.

Step-by-step explanation:

Following mx+b, the m value would be 0.65 because it is added per mile.

The 1.75 would be the b value because it is the starting value.

So the equation would look like 1.75+0.65x. To know if the 10 value would be less than or more than, we have to know if 10 is the limit value or starting value. Because 10 is our limit value, we will use greater than or equal to.

To know how many miles Erica could travel, we would have to subtract 1.75

from 10. We would get 8.25. We would then divide 8.25 by 0.65. so the number of miles she can travel is ~12.7 miles or just 12 miles rounding down.

A store is having a sale where all shoes are discounted by 25%. Diego has a coupon for 2% off of the regular price for one pair of shoes. The store first applies the reduced price. If Diego pays $24.38 for a pair of shoes, what was the original price before the sale and without the coupon?

Answers

Answer:

28.47  sorry if I am wrong

Step-by-step explanation:

Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart below.

Given: m∠LOM = m∠JKI;
m∠MON = m∠IKH
Prove: m∠LON = m∠HKJ

Answers

Answer:

what is the problems from

The difference of a number and its successor

Answers

Answer:

1

Step-by-step explanation:

The difference between a number and its successor is 1

is it
A) X || Z
B) A T Z
C) A || B
D) X T A

Answers

Answer:

Well I would say the answer is A

Step-by-step explanation:

Because there is no metion of line A

Hope this helps have an awsome day!

Given: 5n - 42 = 12n; Prove: n = -6
Statements and reasons

Answers

Answer:

yes n is -6

Step-by-step explanation:

b/c 5(-6)-42=12(-6)

-30-42=-72

-72=-72

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