MHB Is z + z¯ and z × z¯ Real for Any Complex Number z?

Yordana
Messages
3
Reaction score
0
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
 
Physics news on Phys.org
Yep. All correct.
 
Back
Top