(1/2 + 1/3) - (1/2 - 1/3) =

Let z = 2 - 2√3 i. In polar form, we have

[tex]z = |z| e^{i\arg(z)}[/tex]

where

[tex]|z| = |2-2\sqrt3| = \sqrt{2^2 + (-2\sqrt3)^2} = 4[/tex]

[tex]\arg(z) = \tan^{-1}\left(-\dfrac{2\sqrt3}2\right) = -\tan^{-1}(\sqrt3) = -\dfrac\pi3[/tex]

Equivalently,

[tex]z = 4\left(\cos\left(-\dfrac\pi3\right) + i\sin\left(-\dfrac\pi3\right)\right)[/tex]

Let w be a complex number such that w ² = z. By DeMoivre's theorem,

[tex]z = 4\left(\cos\left(-\dfrac\pi3\right) + i\sin\left(-\dfrac\pi3\right)\right) \\\\ \implies z^{1/2} = 4^{1/2} \left(\cos\left(\dfrac{-\frac\pi3+2k\pi}{2}\right) + i \sin\left(\dfrac{-\frac\pi3+2k\pi}{2}\right)\right)[/tex]

where k ∈ {0, 1}. So the two square roots of z are

[tex]z^{1/2} = \begin{cases}2\left(\cos\left(-\dfrac\pi6\right) + i\sin\left(-\dfrac\pi6\right)\right) & \text{for }k=0 \\\\ 2\left(\cos\left(\dfrac{5\pi}6\right) + i\sin\left(\dfrac{5\pi}6\right)\right) & \text{for }k=1\end{cases}[/tex]

[tex]z^{1/2} = \begin{cases}2\left(\dfrac{\sqrt3}2 - \dfrac12 i\right) & \text{for }k=0 \\\\ 2\left(-\dfrac{\sqrt3}2 + \dfrac12 i\right) & \text{for }k=1\end{cases}[/tex]

[tex]\boxed{z^{1/2} = \begin{cases}\sqrt3 - i & \text{for }k=0 \\ -\sqrt3 + i & \text{for }k=1\end{cases}}[/tex]

Answer:

the answer is 8 that is

4/1/2

4÷1/2

4×2/1=

8

Answer:

Answer:

11

Step-by-step explanation:

2+2+1(5)+3+3(6) =11

Answer:

The value of d is -3.

Step-by-step explanation:

We are given that a line that includes the two points (-8, 9) and (-10, d) have a slope of 6. We want to determine the value of d.

Recall that the formula for slope is:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x}[/tex]

We know that the slope is 6. Substitute:

[tex]\displaystyle (6) = \frac{(d) - (9) }{(-10) - (-8)}[/tex]

Solve for d:

[tex]\displaystyle \begin{aligned} 6 & = \frac{d - 9}{-10 + 8} \\ \\ 6 & = \frac{d - 9}{-2} \\ \\ -12 & = d - 9 \\ \\ d & = -3 \end{aligned}[/tex]

In conclusion, the value of d is -3.

Answer:

The x-intercept is (-2 1/7, 0).

The y-intercept is (0, -3).

Step-by-step explanation:

To find the y-intercept, substitute x with zero.

To find the x-intercept, substitute y with zero.

Finding the y-intercept by substituting x with zero:

7*0 + 5y = -15

5y = -15

y = -3

The y-intercept is (0, -3).

Finding the x-intercept by substituting y with zero:

7x + 5*0 = -15

7x = -15

x = -15/7

x = -2 1/7

The x-intercept is (-2 1/7, 0).

Answer:

hello

Step-by-step explanation:

it must be 0,125

hope it helps

Answer:

y = 4x + 4

y = rise/run + y-intercept

Answer:

B. |-6| < |-8|

Step-by-step explanation:

I used a calculator, pls let me know if im incorrect

Answer:

$4.59 would be a good estimate for the dessert with 10% tax.

Step-by-step explanation:

10% = 0.10

0.10 + 4.49

The graph D has a x-intercept = −1  and y-intercept = 5

The given parameters are:

x-intercept = −1

y-intercept = 5

The above means that the graph crosses the x-axis at -1, and it crosses the y-axis at -5

From the list of options, the graph that satisfies the above highlights is graph D

Hence, the graph D has a x-intercept = −1  and y-intercept = 5

Read more about linear graphs at:

https://brainly.com/question/14323743

Answer:

3/2(x+3/4)-x-1

Step-by-step explanation:

Remove the parenthesis

Answer:

Lisas

Step-by-step explanation:

You have to multiply 351X34

then you subtract 10,000, 10,000

Answer:

Step-by-step explanation:

apply the indices law

Answer:

[tex]7x - 24 = 6x - 2 \\ collecting \: like \: terms \: \\ 7x - 6x = - 2 + 24 \\ 1x = 22 \\ x = \frac{22}{1} \: \: or \: \: x = 22[/tex]

Answer:

x = 22

Here's how i got it ^u^

7x - 24 = 6x - 2

Step 1: Subtract 6x from both sides.

 7x - 24 = 6x - 2

- 6x         - 6x

   x - 24 = - 2

Step 2: Add 24 to both sides.

x - 24 = - 2

 + 24   + 24

which TA-DA!!! it equals x = 22

Answer:

Step-by-step explanation:

a) if she had 16 m of fencing

all possible outcomes

4 by 4

2 by 6  

1 by 7

the greatest should be 4 by4

b) she could alter it to 2 by 6

Answer:

One number sentence shows the distributive property of multiplication over addition. ... (5 + 4) × 3 = (5 × 3) + (4 × 3) is an example of the distributive property. (5 − 4) × 3 = 1 × 3. 1 × 3 is not equal to (1 × 3) − (1 × 3).

Step-by-step explanation:

A

Answer:

the answer is 126,321,000

Answer:

Step-by-step explanation:

Lol, so you start by looking at two of your fingers.

You pull up two more fingers.

To find the answer, you add those two numbers (two and two), which gives you four.

Final Answer: 'Four' in words or 4 in numbers.

Hope you found this helpful, or at least amusing.

the answer is: q=3

start by combining like terms (13q - 9q) which would leave you with 4q + 5 = 17. subtract 5 from both sides and you're left with 4q = 12. divide by 4 on both side and you get q = 3

Answer:

q=3

Step-by-step explanation:

13q - 9q + 5 = 17

13q - 9q = 17 - 5

4q = 12

4q/4 = 12/4

q = 3

Answer:

2/3 is right one . option no B

Answer:

See answer I left in previous post

Step-by-step explanation:

164.50+37.50= 201.75

gtu

Yes, It is an improper fraction

Answer:

C) Quadrant 4

Step-by-step explanation:

Hope this helps! Pls give brainliest!