Find the conjugate of

7-3i
8+2i

Find the product and conjugate of
4-i
6+3i

(I am not asking for just the answer I would also like to know how you got that answer)

Answers

Answer 1

Answer:

see below

Step-by-step explanation:

To find the conjugate of a+bi take the opposite of bi so it would be a - bi

7-3i, the conjugate is 7 + 3i

8+2i  the conjugate is 8 -2i

The product of a number and its conjugate is

(a+bi) (a-bi) = a^2 +abi-abi -b^2 i^2 = a^2 - b^2 (-1) = a^2 + b^2

( 4-i) ( 4+i) = 4^2 + 1^2 = 16+1 = 17

( 6+3i)(6-3i) = 6^2 + 3^2 = 36+9 = 45

Answer 2

#1

z=7-3i

[tex]\\ \sf\longmapsto \overline{z}=7+3i[/tex]

#2

z=8+2i

[tex]\\ \sf\longmapsto \overline{z}=8-2i[/tex]

#3

[tex]\boxed{\sf z\overline{z}=|z|^2}[/tex]

[tex]\\ \sf\longmapsto z=4-i[/tex]

[tex]\\ \sf\longmapsto |z|^2=4^2+(-1)^2[/tex]

[tex]\\ \sf\longmapsto 16+1=17[/tex]

#4

[tex]\\ \sf\longmapsto |z|^2[/tex]

[tex]\\ \sf\longmapsto 6^2+3^2[/tex]

[tex]\\ \sf\longmapsto 36+9[/tex]

[tex]\\ \sf\longmapsto 45[/tex]


Related Questions

I need help please .

Answers

Scientific notation is built upon the idea of moving the decimal place to the left or right so many places.

A foundational background concept is that multiplying by 10 makes a number bigger and moves the decimal to the right.
For example: 3.4 x 10 = 34

The counterpart for that is that dividing by 10 makes a number smaller and moves the decimal to the left.
For example: 3.4 ÷ 10 = 0.34

So, when you see 3.4 x 10^5, this means you’re multiplying by 10 fives times, so that will move the decimal point five places to the right.
3.4 x 10^5 = 340 000

On the other hand, when you see a negative exponent on the 10, then that means you’re actually dividing by that many 10s and will move the decimal point that many places to the left. (to make the number smaller)
3.4 x 10^-5 = 0.000034

So, you need to first identify if you’ll make the number bigger or smaller and then how many places the decimal point will need to move.

The middle school band has 600 os members, 200 of the members were chosen for the highly selective All-State Band. What is the value of the ratio of the number of students who were chosen for the All-State Band to the number of students who were not chosen for the All-State Band?​

Answers

Answer: For every three students in band, one will be selected for All-State band.

Step-by-step explanation: The easiest way to explain it is to reduce 600 and 200 by the same number until you can't anymore. I know it sounds like I'm coming up with this off the top of my head, but rest assured that I'm not.

What’s the midpoint of points a (6,-4) and b (2,-10) graphically

Answers

Answer:

here is ur midpoint

Step-by-step explanation:

(4, -7)

Please anything helps. Bisect each angle below
(Don’t know what I was doing on the first one)

Answers

Answer:

U are doing right but don't move ur compass when u are doing the line (i mean opposite line)otherwise ur line at not bisect

Determine whether each equation is always, sometimes, or never true.
2x + 7 - x = 3 + x + 4
Always
Sometimes
Never
Empty Set

I said never but I want see if thats right

Answers

Always because all real numbers are solutions. Please give brainliest.

Write each decimal number as a fraction or mixed number in simplest form?​

Answers

You're letting x = 0.325325325…, which means

1000x = 325.325325325…   (or 325.325, but pretend the underline is actually an overline)

Then the next box you'd fill in with 0.325325325… (or 0.325).

Subtracting these, you have

1000x - x = 325.325325325… - 0.325325325…

999x = 325

Finally, solving for x gives

x = 325/999

Choose the answer that has a value of -8.

A. 6 - (-2)
B. 12 + -4
C. 3 - 5
D. -4 - 4

Answers

Answer:

THE ANSWER IS D

PLEASE GIMME BRAINLIEST BESTIEEE (╥﹏╥)(╥﹏╥)

It’s D
As -+- =-
And value of the greater number is given to the answer as if -4-3=-7 as 4 the greater number has a charge of -

What is the equation of the line that passes through the point (2, -4) and has a
slope of 2

Answers

Answer:

y = 2x - 8    OR     4 - 2x = -4 - y

Step-by-step explanation:

Use the point-slope form m(x₁-x₂) = (y₁-y₂); m means slope

plug in your numbers:

2(2-x₂) = (-4-y₂)

4 - 2x = -4 - y

or to put it into Y=mx + b:

y = 2x + 8

Which equation can be solved for x in the following diagram?

Answers

Answer:

D

Step-by-step explanation:

opposite angles are equal

it would be D because both sides across the line are equal meaning both x values equal 150°

186 div by 20 because i am lost

Answers

Answer:

9.3

Step-by-step explanation:

186/20 = 18.6/2 = 9.3

[tex]Hello[/tex] [tex]There![/tex]

The answer is...

[tex]\frac{93}{10}.[/tex]

Hopefully, this helps you!!

[tex]AnimeVines[/tex]

i need help with 4=2/3(2x-9

Answers

Answer:

x=15/2

Hope it helps :)

Answer:

x = 7.5

Step-by-step explanation:

4 = 2/3 (2x - 9)

4 = 4/3x - 6

4 + 6 = 4/3x - 6 + 6

10 = 4/3x

10 x 3/4 = x

x = 7.5

Here's an easy question for points: 5 x 2/6 =

Answers

Q) 5 × (2/6) = ?

→ 5 × (2/6)

→ 10/6

→ 5/3 {final answer}

This one if to hard for me

Answers

Answer:

x=0 , x = 1/2

Step-by-step explanation:

(4x-1)=1 —> 4x-1=1—> 4x=1+1—> 4x=2 —> x=2/4 —> x= 1/2

-(4x-1)=1—>-4x+1=1—> 4x= 1-1 —> x=0

Hello there!

We are given the equation:

[tex] \displaystyle \large{ |4x - 1| = 1}[/tex]

Definition/Property

[tex] \displaystyle \large{ |a| = \sqrt{ {a}^{2} } } \\ \displaystyle \large{ |a| = b \longrightarrow a = \pm b} \\ \displaystyle \large{ |a| = \begin{cases} a \: \: (x \geqslant 0) \\ - a \: \: (a < 0) \end{cases}}[/tex]

First, cancel the absolute value sign and write plus-minus beside 1.

[tex] \displaystyle \large{ |4x - 1| = 1} \\ \displaystyle \large{ 4x - 1 = \pm 1} \\ [/tex]

Break in two cases.

[tex] \displaystyle \large{ 4x - 1 = \begin{cases} 1 \\ - 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 1 + 1 \\ - 1 + 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 2 \\ 0 \end{cases}} \\ \displaystyle \large{ x = \begin{cases} \frac{2}{4} \\ \frac{0}{4} \end{cases}}[/tex]

Therefore, x = 0 or 1/2

Let me know if you have any questions!

Topic: Absolute Value Function - Equations

True or false: (√2 + √3)^2 = 2 + 3 = 5

Explain:

Answers

Hi! I'm happy to help!

A square root, means:

√x=y

This means that:

x=y·y=√x·√x

When we have the square button, it causes everything to be multiplied by itself once.

√x²=x

Due to the fact that the squared symbol is outside of the parenthesis, it causes both the square toot of 2, and the square root of 3, to be squared.

Now that we know this, √2², and √3²= 2, and 3.

This is why we get 2+3.

2+3=5, which is pretty self explanatory.

I hope this was helpful, keep learning! :D

What is an equation of the line that passes through the points (1, 8) and (-1, -2)

Answers

Answer:

Step-by-step explanation:

(1,8) (-1,-2)

Slope: (-2-8)/(-1-1) = -10/-2 = 5

y -8 = 5 (x - 1)

y - 8 = 5x - 5

y = 5x +3

What is the slope of the line that passes through the points (7,9) and (15,-29)

Answers

Answer:

-4.75

Step-by-step explanation:

Slope = (y2-y1) / (x2-x1)

So applying the formula

(-29-9)/(15-7)

= -38/8 = -4.75

the base of a triangle is 13cm and its height is 5cm. what is the area of the triangle

Answers

Answer:

32.5cm

Step-by-step explanation:

Using the formula A=h_b*b/2

We get 5*13/2=32.5

Gonna post this one last time in hope that someone helps and explains this to me lol.

Answers

Answer: Y = 3500, X = 16

Step-by-step explanation:

Your maximum Y-value is 3000, or, the price of your car, so that could be the answer that's being looked for. However, it's always a good idea to leave a little extra space on the end of the graph so that you can show that your line ends instead of continuing onwards.

Your maximum X-value is 15, or, the number of months it would take to pay off the car (200 dollars per month, until you reach 3000 dollars), but again, it's always smart to leave a little buffer space so that you can see that the graph actually ends.

The answer your teacher wants is probably that the maximum Y-value should be 3000 and the maximum X-value should be 15, but if you have to actually graph this equation yourself and want it to be understood that your graph is a line segment and not a line (the difference being that a line is infinite and a line segment has two ends), you will want to show that by not ending the graph at the same spot as the line segment and instead extending it a little further.

A diver descends at a rate of 4 feet per minute. How far is the diver below sea level after 20 minutes?

Answers

Answer:

4 × 20 = 80 or just add 4 20 times

Solve the following using substitution

Y = 2X - 3

4X -3Y = 31

Answers

Answer:

Step-by-step explanation:

ax+by=c solving for y

Answers

Answer:

[tex]ax + by = c \\ by = c - ax \\ \\ y = \frac{c - ax}{b} \\ \\ y = \frac{c}{b} - \frac{ax}{b} [/tex]

I hope I helped you^_^

by = c - ax
y = (c - ax) / b

|x-3|<2
|4x+1|>0
|x-1|<5
Ayudaaaaaaa pleaseeeee

Answers

Recuerda que

• |x| = x si x ≥ 0

• |x| = -x si x < 0

Necesitas considerar dos casos:

• si x - 3 ≥ 0,

|x - 3| < 1   ⇒  x - 3 < 1   ⇒   x < 4

• si x - 3 < 0,

|x - 3| < 1   ⇒   -(x - 3) = 3 - x < 1   ⇒   -x < -2   ⇒   x > 2

Entonces la solución consta de todos los números reales x tales que x > 2 y x < 4, o simplemente 2 < x < 4.

El método para resolver las otras desigualdades es el mismo.

|4x + 1| > 0   ⇒   4x + 1 > 0   o   -(4x + 1) > 0

…   ⇒   4x + 1 > 0   o   -4x - 1 > 0

…   ⇒   4x > -1   o   -4x > 1

…   ⇒   x > -1/4   o   x < -1/4

⇒   x ≠ -1/4

|x - 1| < 5   ⇒   x - 1 < 5   o   -(x - 1) < 5

…   ⇒   x - 1 < 5   o   -x + 1 < 5

…   ⇒   x < 6   o   -x < 4

…   ⇒   x < 6   o   x > -4

⇒   -4 < x < 6

Remove all perfect squares from inside the square root [tex]\sqrt{200}[/tex]

Answers

It would be 10 square root 2

What are the name of these angles? Are
they congruent or supplementary?

Answers

They are supplementary

-15=5(3q-10)-5q
Solve the equation

Answers

Answer:

q = 3.5

Step-by-step explanation:

Start by distributing the 5

-15 = 15q - 50 - 5q

Combine like terms

-15 = 10q - 50

Add 50 to both sides

35 = 10q

Divide by 10 to isolate q

35/10 = q

q = 3.5

Answer:

q=3.5 or 4

Step-by-step explanation:

-15=5(3q-10)-5q

-5=15q-50-5q

-15+50=15q-5q

35=10q

Divide both sides by 10.

35÷10=10q÷10

3.5=q

Therefore,q= 3.5

Round up=4

.

Find the distance between the two points rounding to the nearest tenth (if necessary).


(−5,−9) and (−8,0)

Answers

The formula is called the “midpoint formula”. It looks like this
m=(x1+x2)/2 , (y1+y2)/2 where m means midpoint. In your case it looks like this.

Write an equation for the following real life scenario.
Use "h" to represent your variable.
Diane worked to earn $48.50 babysitting her neighbors, she earns $6.00 per hour.

Answers

I don't understand the question

When 12 is added to half the sum of a number and 3 the result is 28. What is the number?

Answers

Answer:

29

Step-by-step explanation:

What is the solution to this equation?

2x + 3 (x - 10) = 45

A. x = 15

B. x = 3

C. x = 7

D. x = 11

ANSWER: A (x = 15)

Answers

Answer:

The value of x is 15

Step-by-step explanation:

2x + 3(x - 10) = 45

2x + 3x - 30 = 45

5x - 30 = 45

Now, Add 30 both sides we get,

5x - 30 + 30 = 45 + 30

5x = 75

Now, Divide 5 from both sides we get,

5x/5 = 75/5

x = 15

Thus, The value of x is 15

Hence, Option A is correct

-TheUnknownScientist

helppppppp pleaseeereee
Which number sentence has a product of 42?

7 × (-6)
-6 × 7
-7 × (-6)
-7 × 6

Answers

Answer:

-7 × (-6)

Step-by-step explanation:

7 × (-6) = -42

-6 × 7 = -42

-7 × (-6) = 42

-7 × 6 = -42

Answer:

[tex] - 7 + ( - 6) = 42[/tex]

I hope I helped you^_^

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