postillan4
2021-09-11
Answered

Write down the definition of the complex conjugate, $\stackrel{\u2015}{z}\text{}\text{,if}\text{}z=x+iy$ where z,y are real numbers. Hence prove that, for any complex numbers w and z,

$\stackrel{\u2015}{w\stackrel{\u2015}{z}}=\stackrel{\u2015}{w}z$

You can still ask an expert for help

berggansS

Answered 2021-09-12
Author has **91** answers

Step 1

Complex consugate

Let z be a complex number defined by

complex consugate of z is the sum change of imaginary part.

let

Step 2

Form equation 1 and equation 2

asked 2021-09-08

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.

$P\left(x\right)=-12{x}^{2}+2136x-41000$

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

asked 2021-02-05

Use polar coordinates to find the limit. [Hint: Let $x=r\mathrm{cos}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r\mathrm{sin}$ , and note that (x, y) (0, 0) implies r 0.]
$\underset{(x,y)\to (0,0)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}$

asked 2022-01-07

Prove multivariable function is surjective

The function is

asked 2021-09-22

Engineering company has a task of checking compressive strength for 100 concrete cubes. The results revealed that 85 cubes passed the compressive strength test successfully and 15 cubes failed in the test. If 10 cubes are selected at random to be inspected by the company, determine the probability that the 8 cubes will pass the test
and 2 cubes will fail in the test by using the Combinatorial Analysis.

a. 0.4522

b. 0.3415

c. 0.6553

d. 0.1156

e. 0.2919

a. 0.4522

b. 0.3415

c. 0.6553

d. 0.1156

e. 0.2919

asked 2021-01-15

Evaluate the line integral by the two following methods. y) dx + (x+y)dy C os counerclockwise around the circle with center the origin and radius 3(a) directly (b) using Green's Theorem.

asked 2022-01-04

How to find expressions for $f}_{xx$ and $f}_{yy$ for the multivariable function $f(x,y)=\mathrm{ln}\left({x}^{2}y\right)+{y}^{3}{x}^{2}$ ?

asked 2022-01-04

How do you define iterations of multivariable functions?

To be clear(example):

If$f:{\mathbb{R}}^{2}\to \mathbb{R}$

How do you define

$f\circ f,\text{or}f\circ \dots \circ f?$ ?

To be clear(example):

If

How do you define