Check for any complex number z

[Yordana]

I apologize in advance for my English.
I want to know if my solution is correct. :)

To verify that for every complex number z, the numbers z + z¯ and z × z¯ are real.

My solution:
z = a + bi
z¯ = a - bi
z + z¯ = a + bi + a - bi = 2a ∈ R
z × z¯ = (a + bi) × (a - bi) = a^2 + b^2 ∈ R

 

[I like Serena]

Yep. All correct.