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Westkost [7]
3 years ago
11

...........................................

Business
1 answer:
Novay_Z [31]3 years ago
3 0
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Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers. We say that $z \in S$ is a unit if t
lakkis [162]

Answer:

Number of units possible in S are 4.

Explanation:

Given <em>S</em> is a set of complex number of the form a+bi where <em>a</em> and <em>b</em> are integers.

z\in S is a unit if w\in z exists such that zw=1.

To find:

Number of units possible = ?

Solution:

Given that:

zw = 1

Taking modulus both sides:

|zw| = |1|

Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.

i.e.

|z_1z_2|=|z_1|.|z_2|

So,

|zw| = |1|\\\Rightarrow |zw| =|z|.|w| =1\\\Rightarrow |z|=\dfrac{1}{|w|}......... (1)

Let z=a+bi

Then modulus of z is   |z| = \sqrt{a^2+b^2}

Given that a and b are <em>integers</em>, so the equation (1) can be true only when |z| = |w| =1 (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:

(a = 1, b = 0) ,  (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)

So, the possible complex numbers can be:

1.\ 1 + 0i = 1\\2.\ -1 + 0i = -1\\3.\ 0+ 1i = i\\4.\ 0 -1i = -i

Hence, number of units possible in S are 4.

6 0
3 years ago
Was the time period between 400ad and 1400ad a dark age for europe? was this a time of cultural decay and decline?
eduard

AD was a dark age and a period of cultural decay and decline for Europe because there was barely a government, harsh punishments, ignorant people, not a lot of land, and there was a lot of killing and diseases going around Europe that cause Europe to decline in population.

8 0
3 years ago
This chart shows the link between interest in a product and the price a consumer pays.
mr Goodwill [35]

<u>Answer: </u>

The given chart shows the link between interest in a product and the price a consumer pays.

<u>Explanation: </u>

  • The more the interest a person has in a product, the more willing he is to pay any demanded price for the product.
  • On the other hand, if a person is not at all interested in a specific product, he would not buy it even if it is available at the cheapest price in the market.
3 0
3 years ago
Read 2 more answers
extreme weather in new york, where the super bowl is scheduled to be played, makes people disinterested in purchasing super bowl
alexira [117]

The following scenarios would place a downward pressure on price:

  1. .The Nile River floods this year add an exceptional amount of silt to the soil, resulting in increased crops of cotton.
  2. An outbreak of mad cow disease causes Americans to abstain from eating beef.
  3. Extreme weather in New York, where the Super Bowl is scheduled to be played, makes people disinterested in purchasing Super Bowl tickets.

The following scenarios would place a downward pressure on price:

An impending unclear holocaust causes people to stock up on twonkies, a popular snack cake provided by many companies

<h3>What would lead to either a upward or downward pressure on price?</h3>

There is an upward pressure on price if demand increases or supply reduces. There is a downward pressure on price if demand decreases or supply increases.

As a result of the slit, there would be an increase in the supply of cotton. This would lead to an downward pressure on price. The mad cow disease would lead people to demand less beef. This would lead to an downward pressure on price. The extreme weather would lead to people not coming for the game. This would lead to an downward pressure on price.

Due to the expectation of the holocaust, there would be an increased demand for twonkies. This would lead to an upward pressure on price.

Here is the complete question:

Decide whether each scenario would lead to upward or downward pressure on the equilibrium price for each good in bold font.

1.The Nile River floods this year add an exceptional amount of silt to the soil, resulting in increased crops of cotton.

2.An outbreak of mad cow disease causes Americans to abstain from eating beef.

3. Extreme weather in New York, where the Super Bowl is scheduled to be played, makes people disinterested in purchasing Super Bowl tickets.

4. An impending unclear holocaust causes people to stock up on twonkies, a popular snack cake provided by many companies

For more information about the change in demand, please check: brainly.com/question/25871620

#SPJ1

3 0
1 year ago
A pizza monopolist employing third-degree price discrimination charges students $10 per pizza and everyone else $15 per pizza St
tangare [24]

Answer:

The price elasticity of demand for the students is:

inelastic.

Explanation:

The price elasticity of demand for the students is inelastic because there is no change in the quantity demanded by students that changes the price at which pizza is sold to the students.  If one student buys the pizza, the price charged remains $10 and if 1,000 students buy the pizza, the price remains $10 per unit.  Therefore, students' demand for the pizza is said to be static irrespective of price because the price is fixed.

8 0
2 years ago
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