Question

For this exercise, you need a definition of absolute value of a complex number.

Answer 1

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.

Answer 2

True

Explanation:

because if you have q+i=p then that would be a true complex but in this case it would be true because of absolute value