15 points for correct ! given that x = 4 + 5i and y = 2 - 9i, match the equivalent expressions.

As it has been given that , .

We need to find the value of the following:

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

So,

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

So,

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

Using the distributive property of multiplication:

Now, we know that

We get,

Therefore, =.

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

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

So,

since,

we get,

Therefore,

x=6 and x=3

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