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)

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+xTaking 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=LHSTaking 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=LHSTaking 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 truev) (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=LHSTaking 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 trueTherefore the statements i), iv) and v) are true