For statement one:
We need to add up to complex numbers and their sum must give us equal to 10.
Also, we need to use the complex numbers:
5+i√15 and 5-i√15.
Then, we can use:
(5+i√15)+( 5-i√15) =
5+i√15+5-i√15 =
5+5+ i√15-i√15 =
= 10 + 0
= 10
For the second statement:
We need to show the product of complex numbers:
Then, we use:
(5+i√15)(5-i√15))=
5*5 - 5*i√15) +5*i√15) +√15*√15=
25 + 0 + 15=
40