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tigry1 [53]
2 years ago
14

Let x = a bi and y = c di and z = f gi which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x ×

(y × z) x – y = y – x (x y) z = x (y z) (x – y) – z = x – (y – z)
Mathematics
1 answer:
Alex73 [517]2 years ago
6 0

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

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