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FinnZ [79.3K]
3 years ago
14

PLEASE HELP HURRY!!!!!!!

Mathematics
2 answers:
Charra [1.4K]3 years ago
7 0

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


White raven [17]3 years ago
3 0

x•y = 53-26i 2x•y = 106-52i

-x+3y= 2-32i

4x-y = 14+39i

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