Question

PLEASE HELP HURRY!!!!!!!

Answer 1

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:

$4(4+5i)-(2-9i)=4\times 4+4\times 5i-2+9i=16+20i-2+9i$

$=14+29i$

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

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

$-(4+5i)+3(2-9i)=-4-5i+3\times 2-3 \times 9i=-4-5i+6-27i$

$=2-32i$

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

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

$a(b+c)=a \times b+ a \times c$

Using the distributive property of multiplication:

$(4+5i)\times(2-9i)=4 \times 2-4 \times 9i+5i \times 2-5i \times 9i$

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

Now, we know that $i \times i=i^2=-1$

We get, $8-36i+10i-45 \times (-1)=8-26i+45$

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

Therefore, $x \times y$=$53-26i$.

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

$2(4+5i)\times (2-9i)$

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

$a(b+c)=a \times b+ a \times c$

So,

$2(4+5i) \times (2-9i)=2\times 4+2 \times 5i\times(2-9i)$

$=8+10i \times(2-9i)=8\times 2-8 \times 9i+10i \times 2-10i \times 9i$

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

since, $i^2=-1$

we get,

$16-72i+20i-90 \times (-1)=16-52i+90$

$=106-52i$

Therefore,

$2x \times y=106-52i$

Answer 2

x•y = 53-26i 2x•y = 106-52i

-x+3y= 2-32i

4x-y = 14+39i