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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 S is a set of complex number of the form $a+bi$ where a and b 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 integers, 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

Jimmy, the marketing manager for an automobile manufacturer, observes frequent conflicts between two of his subordinates, Trent

Alina [70]

it is the person analysis

reason-

a person analysis is the analysis in whch we study the behaviour of the employees it helps us to identify the employees who lacks skills or need training.

8 0

3 years ago

A point outside (to the right of) the production possibilities curve of a nation implies that this nation is using its resources

PtichkaEL [24]

Answer:

is not attainable for this nation

Explanation:

The Production possibilities frontiers is a curve that shows the various combination of two goods a company can produce when all its resources are fully utilised.

The PPC is concave to the origin. This means that as more quantities of a product is produced, the fewer resources it has available to produce another good. As a result, less of the other product would be produced. So, the opportunity cost of producing a good increase as more and more of that good is produced.

Point outside the curve or to the right of the curve means that the production level is not attainable given the level of resources

Points inside the production possibilities curve means that the nations resources are not being fully utilised

Factors that cause the PPF to shift

1. changes in technology.

2. changes in available resources.

3. changes in the labour force.

8 0

3 years ago

Next Up Computer Company thinks it will make a splash with cartoon-themed laptop cover designs scheduled for release next year.

vova2212 [387]

Considering the situation described above, this effort is an example of using image differentiation to differentiate a product as new.

Image differentiation is a type of differentiation strategy used by business firms to differentiate their products through communications.

By using communication strategies such as written, audio, digital, advertisement, or images to differentiate between various products or from existing products, this is an example of image differentiation.

Thus, when Next Up Computers only changes the cover designs alone, that is a form of image differentiation.

This is type of differentiation is often referred to as Reputation Differentiation.

Other types of differentiation methods include the following:

Product differentiation
Service differentiation
Relationship differentiation
Distribution differentiation.
Price differentiation.

Hence, in this case, it is concluded that the correct answer is "Image Differentiation."

Learn more here: brainly.com/question/14302620

6 0

3 years ago

Gundy Company expects to produce 1,213,200 units of Product XX in 2020. Monthly production is expected to range from 80,000 to 1

fiasKO [112]

Answer:

Gundy Company

Flexible Budget Report for March 2020:

Actual Budget Flexible Budget Variance

Direct materials $515,000 $485,000 $30,000 U

Direct labor 670,000 679,000 9,000 F

Variable overhead 1,073,000 1,067,000 6,000 U

Actual fixed costs 679,000 679,000 0 None

Total costs incurred $2,937,000 $2,910,000 $27,000 U

Explanation:

a) Data and Calculations:

Expected production of Product XX in 2020 = 1,213,200 units

Monthly production range = 80,000 to 114,000 units

Budgeted variable manufacturing costs per unit are:

Direct materials $5

Direct labor $7

Overhead $11

Total variable $23

Fixed manufacturing costs per unit:

Depreciation are $6

Supervision are $1

Total fixed costs $7

Total costs = $30

March 2020 costs incurred for 97,000 units:

Direct materials $515,000

Direct labor $670,000

Variable overhead $1,073,000

Actual fixed costs 679,000

Total costs incurred $2,937,000

Flexible Budget Report for March 2020:

Actual Budget Flexible Budget Variance

Direct materials $515,000 $485,000 $30,000 U

Direct labor 670,000 679,000 9,000 F

Variable overhead 1,073,000 1,067,000 6,000 U

Actual fixed costs 679,000 679,000 0 None

Total costs incurred $2,937,000 $2,910,000 $27,000 U

4 0

3 years ago