SOLUTION: (1-4i)ˆ2 + 3 + (8i) - (-2-7i) how do I simplify this? Thank you.

Algebra ->  Sequences-and-series -> SOLUTION: (1-4i)ˆ2 + 3 + (8i) - (-2-7i) how do I simplify this? Thank you.       Log On


   

Question 766639: (1-4i)ˆ2 + 3 + (8i) - (-2-7i) how do I simplify this? Thank you.
Found 2 solutions by lwsshak3, Shana-D77:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
simplify:
(1-4i)ˆ2 + 3 + (8i) - (-2-7i)
1-8i+16i^2+3+8i+2+7i
1-8i-16+3+8i+2+7i
-10+7i

Answer by Shana-D77(132) About Me  (Show Source):
You can put this solution on YOUR website!
the hardest part is simplifying (1-4i)ˆ2:
Let's first remember...
i = sqrt(-1)
i^2 = -1
i^3 = -(sqrt(-1))
i^4 = 1


(1-4i)ˆ2 = (1-4i)(1-4i) = 1 - 4i - 4i + 16i^2
Since i^2 = -1, the above simplifies to: 1 - 8i - 16
Which simplifies to: -15 - 8i


Now add in the rest of the problem:
-15 - 8i + 3 + (8i) - (-2-7i)
-15 - 8i + 3 + 8i + 2 + 7i (distributed the - outside (-2-7i))
-10 + 7i (combined like terms)