Question

PLEASE HELP HURRY!!!!!!!

15 POINTS FOR CORRECT ANSWER!!!!!

Given that x = 4 + 5i and y = 2 - 9i, match the equivalent expressions.

Answer 1

x•y = 53-26i 2x•y = 106-52i

-x+3y= 2-32i

4x-y = 14+39i

Answer 2

As it has been given that
`x=4+5i`,
`y=2-9i`.

We need to find the value of the following:

(i)
`4x-y`, substituting the value of 'x' and 'y' in the expression, we get:

`4(4+5i)-(2-9i)=4* 4+4* 5i-2+9i=16+20i-2+9i`

`=14+29i`

So,
`4x-y=14+29i`

(ii)
`-x+3y`, substituting the value of 'x' and 'y' in the expression, we get:

`-(4+5i)+3(2-9i)=-4-5i+3* 2-3 * 9i=-4-5i+6-27i`

`=2-32i`

So,
`-x+3y=2-32i`

(iii)
`x * y`, we need to substitute the value of 'x' and 'y' in the expression, for this, we can use distributive property of multiplication that says,

`a(b+c)=a * b+ a * c`

Using the distributive property of multiplication:

`(4+5i)*(2-9i)=4 * 2-4 * 9i+5i * 2-5i * 9i`

`=8-36i+10i-45i^2`

Now, we know that
`i * i=i^2=-1`

We get,
`8-36i+10i-45 * (-1)=8-26i+45`

`=8+45-26i=53-26i`

Therefore,
`x * y`=
`53-26i`.

(iv) We have,
`2x * y`, we need to substitute the value of 'x' and 'y' in the expression, we get:

`2(4+5i)* (2-9i)`

Again, we can use distributive property of multiplication that says,

`a(b+c)=a * b+ a * c`

So,

`2(4+5i) * (2-9i)=2* 4+2 * 5i*(2-9i)`

`=8+10i *(2-9i)=8* 2-8 * 9i+10i * 2-10i * 9i`

`=16-72i+20i-90i^2`

since,
`i^2=-1`

we get,

`16-72i+20i-90 * (-1)=16-52i+90`

`=106-52i`

Therefore,

`2x * y=106-52i`