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Alexxx [7]
3 years ago
7

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

here exists a $w \in S$ such that $zw = 1.$ Find the number of units in $S.$
Business
1 answer:
lakkis [162]3 years ago
6 0

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.

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Praxis Corp. forecasts the following income statement for the next year:
Annette [7]

Answer: a. 1.42

b) 2.74

c) 3.89

Explanation:

a) The Degree of Operating Leverage measures how much operating Income will change by if Sales change.

It is calculated with the formula,

= (Sales - Variable Costs) / (Sales - Variable Costs - fixed costs)

= (960,000 - 532,000) / (960,000 - 532,000 - 127,000)

= 1.42

b) The Degree of financial leverage measures how much Income will change due to a change in operating Income.

The formula is,

=Earnings before Interest and tax / Earnings before Interest and tax - Interest or just Earning before tax

= 301,000/110,000

= 2.74

c. Degree of Total Leverage is a measure of how sensitive the net income of a company is to a change in goods produced and/or sold.

It is calculated by multiplying DOL and DFL.

= 1.42 * 2.74

= 3.89

Should you need any clarification just hit that comment button. Cheers.

3 0
3 years ago
Amounts collected by the lender and held in a trust or impound account for future payment are called what?
Aleonysh [2.5K]

The amounts collected by the lender and held in a trust or impound account for future payment are called Reserves.

Reserves are earnings that have been appropriated or set apart, for use for a selected cause in addition down the road. A few examples of specific reserves include capital redemption reserves, contingency reserves, debenture redemption reserves, and dividend equalization reserves. each of these reserves has a particular purpose, but, if important, specific reserves can every so often be used for bills that are not their meant functions.

Reserves may be funded by way of annual working surpluses, or thru a funding plan. These price ranges are considered to be "savings bills" so no fees can be charged without delay to them; the simplest transfer object codes must be utilized to reserve money owed.

A lender is a man or woman, a set (public or non-public), or an economic institution that makes finances available to a person or business with the expectation that the price range could be repaid. Compensation will include the charge of any hobby or costs.

Learn more about economic institutions here brainly.com/question/4230044

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5 0
1 year ago
A politician is interested in the proportion of voters in his district who think he is doing a good job.
MaRussiya [10]

A politician should be interested in the proportion of voters in his district.

The answer is true.

Explanation:

This is not only true for politician but also for any job which involves voting.

A person / leader will be recognized, if he

  • look into the welfare of the society
  • takes measure when problem occurs
  • is easily accessible to the public
  • lend his ears to the problems
  • provides an unbiased approach
  • he is interested in doing service
  • obeys laws

But it does not mean that, the person who got victory in the election has done good job in the previous service period. There are many factors that decide the polling of vote.

3 0
3 years ago
Should you include personal date on a resume ? explain your answer?​
yan [13]
No, you should not.

Explanation:

It’s illegal for employers to ask for that data.
8 0
2 years ago
Read 2 more answers
I dont have to pay for this right?
olga nikolaevna [1]

Answer:

no

Explanation:

7 0
3 years ago
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