Carol was given three numbers and
was asked to add the largest of the
three to the product of the other two.
Instead, she multiplied the largest with
the sum of the other two, but still got
the right answer. What is the sum of
the three numbers?
Prove that two straight lines with
complex slopes μ_1 and μ_2 are parallel
and perpendicular according as μ_1 = μ_2
and μ_1 + μ_2 = 0. Hence if the straight
lines α^ z + αz^ + c = 0 and β^ z + βz^ + k = 0
are parallel and perpendicular according
as α^ β − αβ^ = 0 and α^ β + αβ^ = 0.