Further maths help needed!!!

Calculate (2+i sqrt5)(sqrt5-i)

I got that it = 3sqrt5+3i.

Hence verify that sqrt5 - i is a root of the equation (2+i sqrt5)z=3z* where z* is the complex conjugate of z

Could someone give me some guidance on how to answer this question

Can you post your working?

You should be able to substitute into the LHS and show you get the RHS but check expansion.

show my working for the calculation or the verification of roots?

The expansion first.

2 sqrt 5 - 2i + 5i - i^2 sqrt5
= 3 sqrt5 +3i

So what have you got for z*

would it be 5+i?

Isn't z = sqrt5 - i

Right yes, so the complex conjugate would be sqrt5 + i
How do I show it is a root of (2+i sqrt5)z=3

Given that the expansion 3root5 +3i, factor the 3 out and you should be done!

Are you sure? How does that show that sqrt5 - i is a factor?

Are you sure? How does that show that sqrt5 - i is a factor?

You are trying to show that the conjugate is a factor

Look at the LHS - that is just what you expanded if you sub in z. Write LHS = and get an answer

Ten work out the RHS and show the two expressions are identical - that proves it.