Question

how is 7-3i + 7+3i = 14/1
we're doing sum and product of roots, and i don't get how this is equal to 14

Answer 1

sorry i needed to add more info for this to make sense
the problem is asking to write the quadratic equation that has those roots.
so in this case i'd use those roots to find -b/a
but i don't get how that correlates to -b/a?

Answer 2

if you want a quadratic that has 7-3i and 7+3i as roots, build it the way you normally do

say the roots were 3 and -2.You would say
y = (x-3)(x+2)

so, here we have

y = (x-(7-3i))(x-(7+3i))

looks messy, but with a little regrouping, and recalling that (a-bi)(a+bi) = a^2+b^2,

y = ((x-7)-3i)((x-7)+3i)
= (x-7)^2 + 9
= x^2 - 14x + 58