please help with this math problem?

Question

i need help understanding the steps to solving this problem :|

evaluate 6z - z^2 if z = 4 - 3i

ok but, dont i have to factor the ^2

so it would be 6(4-3i)-(4-3i)^2, which would be
6(4-3i)-(4-3i)(4-3i)???

and in that case i tried but came up with the wrong answer

thanks pb great help!

and nate yea, it was witha + sign, and not - thanks!

Answer 1

z (6 - z)
z (2 + 3 i)
(4 - 3 i) (2 + 3 i)
8 + 6 i + 9
17 + 6 i

Answer 2

do a straight-out multiplication!

6z - z^2 if z = 4 - 3i means
6(4-3i) - (4-3i)^2
= 24 -18i - (16 - 4*3i + 9i^2 ), right? simplify
= 24 -18i - (16 - 4*3i -9 ), since i^2 = -1. simplify some more
= 24 -18i - ( 7 - 12i), drop parens, note signs
= 24 -18i - 7 + 12 i, gather
= 17 - 6i. Done.

Answer 3

6(4-3i) - (4-3i)^2
(24-18i) - ((4-3i) x (4-3i))
24-18i - (16 -24i + 9i^2)
8 + 6i - 9i^2

I think thats what it is. Depends on if i is a random variable or -1. If its -1 the answer should be 17 + 6i.

Answer 4

replace the variable z with (4-3i) and see if that helps.

Answer 5

6z -- z^2
= 6(4 + 3i) -- (4 + 3i)^2 .................. put z = 4 + 3i
= 24 + 18i -- 16 -- 24i + 9 .................... i^2 = -- 1
= 17 -- 6i