Question

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)

Answer 1

Answer:A, B, D

Step-by-step explanation:

EDG

Answer 2

Answer:

The statements i) x+y=y+x

,iv) (x+y)+z=x+(y+z)

and v) (x-y)-z = x-(y-z) are true

Step-by-step explanation:

Given that  x = a + bi and y = c + di and z = f + gi

To check which statements are true :

i)x+y=y+x

Taking LHS x+y

Substitute the values of x and y we get

x+y=a+bi+c+di

x+y=(a+c)+(b+d)i=LHS

Taking RHS y+x

Substitute the values of x and y we get

• y+x=c+di+a+bi
• y+x=(c+a)+(d+b)i
• y+x=(a+c)+(b+d)i=RHS
• Therefore LHS=RHS

Therefore x+y=y+x statement is true

iv) (x+y)+z=x+(y+z)

Taking LHS (x+y)+z

Substitute the values of x ,y and z we get

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

(x+y)+z=(a+c+f)+(b+d+g)i=LHS

Taking RHS x+(y+z)

Substitute the values of x ,y and z we get

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

x+(y+z)=(a+c+f)+(b+d+g)i=RHS

Therefore LHS=RHS

Therefore  statement (x+y)+z=x+(y+z) is true

v) (x-y)-z = x-(y-z)

Taking LHS (x-y)-z

Substitute the values of x ,y and z we get

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

=a+bi-c-di-f-gi

(x-y)-z=(a-c-f)+(b-d-g)i=LHS

Taking RHS x+(y+z)

Substitute the values of x ,y and z we get

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

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

Therefore LHS=RHS

Therefore  statement (x-y)-z=x-(y-z) is true

Therefore the statements i) ,iv) and v) are true