p=1+2i, q=1-2i, p+q=2, pq=1²+2²=5, |p|=|q|=√5
p=3-i, q=3+i, p+q=6, pq=3²+1²=10, |p|=|q|=√10
p=-6+8i, q=-6-8i, p+q=-12, pq=(-6)²+8²=100, |p|=|q|=10
b.
The sum of conjugates is twice the real part.
The product of conjugates is the squared magnitude.
Conjugates have the same magnitude.
The difference of conjugates is 2i times the imaginary part.
c.
TRUE.
Let p=a+bi
(-p)* = (-(a+bi))* = (-a-bi)* = -a + bi
-(p*) = -(a-bi) = -a + bi
They're the same.
