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Daniel [21]
2 years ago
9

What is the tan invers of 3i/-1-i​

Mathematics
1 answer:
postnew [5]2 years ago
6 0

<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )

<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )

<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)

<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)

<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))

<em>z</em> = (-3 - 3<em>i </em>) / 2

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

arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>

arg(<em>z</em>) = arctan(1) - <em>π</em>

arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>

arg(<em>z</em>) = -3<em>π</em>/4

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

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Step-by-step explanation:

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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
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kondor19780726 [428]

Answer:

A)

Step-by-step explanation:

youjust have to do this:

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x= 150 miles

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Vedmedyk [2.9K]

Answer:

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Step-by-step explanation:

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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

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22 ÷ 35 = 0.628  ≅ 0.63

6 1
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