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2 years ago

What is the tan invers of 3i/-1-i

Mathematics

1 answer:

postnew [5]2 years ago

6 0

z = 3i / (-1 - i )

z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )

z = (3i × (-1 + i )) / ((-1)² - i ²)

z = (-3i + 3i ²) / ((-1)² - i ²)

z = (-3 - 3i ) / (1 - (-1))

z = (-3 - 3i ) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have

arg(z) = arctan((-3/2)/(-3/2)) - π

arg(z) = arctan(1) - π

arg(z) = π/4 - π

arg(z) = -3π/4

where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.

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3 years ago

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2 years ago

Cloud nine is having a sale on all shirts and pants in the store.Olivia purchased 8 shirts 4 pairs of pants for $176.Raheem purc

mihalych1998 [28]

Question is Incomplete; Complete question is given below;

Cloud Nine is having a sale on all shirts and pants in the store. Olivia purchased 8 shirts and 4 pairs of pants for $176. Raheem purchased 3 shirts and 4 pairs of pants for $116. Let x represent the price of a shirt and y represent the price of a pair of pants. Write a system of equations, and use the elimination method to find a reasonable price for a pair of pants.

Answer:

The system of equations are $\left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.$

The reasonable price for pair of pants is $20.

Step-by-step explanation:

Let the price of shirt be 'x'.

Let price of pair of pants be 'y'.

Given:

Olivia purchased 8 shirts 4 pairs of pants for $176

So we can say that;

8 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 176.

framing in equation form we get;

$8x+4y=176 \ \ \ \ equation \ 1$

Also Given:

Raheem purchased 3 shirts and 4 pairs of pants for 116.

So we can say that;

3 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 116.

framing in equation form we get;

$3x+4y=116 \ \ \ \ equation \ 2$

Hence the system of equation are $\left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.$

Now by using elimination method we will subtract equation 2 from equation 1 we get;

$(8x+4y)-(3x+4y)=176-116\\\\8x+4y-3x-4y = 60\\\\5x =60\\\\x=\frac{60}{5}=\$12$

Now Substituting the value of x in equation 1 we get;

$8x+4y=176\\\\8\times 12+4y =176\\\\96+4y=176\\\\4y =176-96\\\\4y = 80\\\\y= \frac{80}{4} =\$ 20$

Hence The reasonable price for pair of pants is $20.

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2 years ago

Which of the following high speed trains are traveling at a rate of 150 miles per hour? A: a train that travels 100 miles in 2/3

kondor19780726 [428]

Answer:

Step-by-step explanation:

youjust have to do this:

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3 years ago

As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship be

Vedmedyk [2.9K]

Answer:

0.63

Step-by-step explanation:

To get the relative frequency of students with red hair, we need to find the relative frequency of students with red hair from the students with gray eyes.

Since we already know that the total number of students with gray eyes is 35 and the number of red hair students with gray eye is 22

The formula we will use to calculate the relative frequency will be

The relative frequency of students with red hair = Total students of red hair with gray eyes divide by total number of gray eye students

22 ÷ 35 = 0.628 ≅ 0.63

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3 years ago

What is the tan invers of 3i/-1-i​

What is the tan invers of 3i/-1-i