How do i graph x + y = 3

A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.

<h3>What is a Complex Number?</h3>

A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.

As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.

A.) x+y=y+x

$x+y=y+x\\a+bi+c+di=c+di+a+bi$

As the two sides of the equation are equal, the equation is true.

B.) (x × y) × z = x × (y × z)

$(x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)$

$(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\\\\\\acf+adfi+bcfi-bdf+acgi-adg-bcg-bdgi = acf+acgi+afdi-adg + bcfi-bcg-bfd-bdgi$

As the two sides of the equation are equal, the equation is true.

C.) x−y=y−x

$x-y=y-x\\\\(a+bi)-(c+di)=(c+di)-(a+bi)\\\\a+bi-c-di=c+di-a-bi$

As the two sides of the equation are not equal, the equation is not true.

D.) (x+y)+z=x+(y+z)

$(x+y)+z=x+(y+z)\\\\(a+bi+c+di)+f+gi = a+bi+(c+di+f+gi)\\\\a+bi+c+di+f+gi = a+bi+c+di+f+gi$

As the two sides of the equation are equal, the equation is true.

E.) (x−y)−z=x−(y−z)

$(x-y)-z=x-(y-z)\\\\(a+bi-c-di)-f-gi = a+bi-(c+di-f-gi)\\\\a+bi-c-di-f-gi =a+bi-c-di+f+gi)$

As the two sides of the equation are not equal, the equation is not true.

Hence, all the statements are true except C and E.

Learn more about Complex Number:

brainly.com/question/12464608

6 0

2 years ago

A random sample of n = 8 E-glass fiber test specimens of a certain type yielded a sample mean interfacial shear yield stress of

ANTONII [103]

Answer:

$32.9-2.365\frac{4.9}{\sqrt{8}}=28.80$

$32.9+2.365\frac{4.9}{\sqrt{8}}=37.00$

Step-by-step explanation:

Information given

$\bar X=32.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=8 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

the degrees of freedom are given by:

$df=n-1=8-1=7$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and the critical value for this cae would be $t_{\alpha/2}=2.365$

Now we have everything in order to replace into formula (1):

$32.9-2.365\frac{4.9}{\sqrt{8}}=28.80$

$32.9+2.365\frac{4.9}{\sqrt{8}}=37.00$

6 0

3 years ago