Answer:
<h3>The statements i) x+y=y+x</h3><h3> ,iv) (x+y)+z=x+(y+z)</h3><h3>and v) (x-y)-z = x-(y-z) are true </h3>
Step-by-step explanation:
Given that x = a + bi and y = c + di and z = f + gi
<h3>To check which statements are true :</h3><h3>i)x+y=y+x</h3><h3>Taking LHS x+y</h3>
Substitute the values of x and y we get
x+y=a+bi+c+di
<h3>x+y=(a+c)+(b+d)i=LHS</h3><h3>Taking RHS y+x</h3>
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
<h3>Therefore x+y=y+x statement is true </h3><h3>iv) (x+y)+z=x+(y+z)</h3><h3>Taking LHS (x+y)+z</h3>
Substitute the values of x ,y and z we get
(x+y)+z=(a+bi+c+di)+(f+gi)
<h3>(x+y)+z=(a+c+f)+(b+d+g)i=LHS</h3><h3>Taking RHS x+(y+z)</h3>
Substitute the values of x ,y and z we get
x+(y+z)=(a+bi)+(c+di+f+gi)
<h3>x+(y+z)=(a+c+f)+(b+d+g)i=RHS</h3>
Therefore LHS=RHS
<h3>Therefore statement (x+y)+z=x+(y+z) is true</h3><h3>v) (x-y)-z = x-(y-z)</h3><h3>Taking LHS (x-y)-z</h3>
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
<h3>(x-y)-z=(a-c-f)+(b-d-g)i=LHS</h3><h3>Taking RHS x+(y+z)</h3>
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
<h3>Therefore statement (x-y)-z=x-(y-z) is true</h3><h3>Therefore the statements i) ,iv) and v) are true </h3><h3 />
