NOTE: The z in red below has a bar line over it.
Use the rule z times z = a^2 + b^2 to solve the question below when z = 3 - 4i and w = 8 + 3i.
Solve z times z =
ok, i have no idea where you are getting (x + 3) and (x - 2) from. are you leaving out a part of the question?
the rule is: if $\displaystyle z = a + ib$
then
(1) $\displaystyle z^2 = (a + ib)(a + ib) = a^2 - b^2 + 2abi$
(2) $\displaystyle |z|^2 = a^2 + b^2$
where are your x's coming from?
EDIT: Oh! i see now, you put red z to mean $\displaystyle \bar{z}$!
ok, so $\displaystyle z \bar{z} = (a + ib)(a - ib) = a^2 + b^2 = |z|^2$
still, where are you getting your x's from?!
What you need to do is go back and read the question CAREFULLY.
For one thing it surely does not say "write the QUESTION in the form a+bi". Perhaps it says "write the ANSWER in the form a+ bi.
But then "5(x+ 3)(x-2)^2(x+1)" is NOT in the form a+ bi!
As you said before $\displaystyle z\overline{z}= 3^2+ (-4)^2$, a positive real number, not some product of algebraic expressions. Perhaps you accidently looked up the answer to the wrong question.