SOLUTION: Perform the indicated operations and write the answer in standard form: (4-i)^2+2(3-2i)-4 I don't even know where to begin. Help! Do I take care of what is inside the parenthes

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Perform the indicated operations and write the answer in standard form: (4-i)^2+2(3-2i)-4 I don't even know where to begin. Help! Do I take care of what is inside the parenthes      Log On


   

Question 29568: Perform the indicated operations and write the answer in standard form: (4-i)^2+2(3-2i)-4 I don't even know where to begin. Help! Do I take care of what is inside the parenthesis first?
Mary
Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
(4-i)^2+2(3-2i)-4
=[(4)^2+2X(4)X(-i)+(-i)^2]+[2X3-2X(3i)]-4
[using (a+b)^2 = a^2 +2ab+b^2 where here a = 4 and b= (-i)]
=[16-8i+i^2]+6-4i-4
=(16-8i-1)+6-4i-4
=(16-1+6-4)+(-8i-4i) (grouping like terms)
=17-12i
Answer: (4-i)^2+2(3-2i)-4 = 17-12i
Note:(4-i)^2 can also be expanded using
(a-b)^2 = a^2-2ab+b^2 where here a=4,b= i and therefore
a^2 = 4^2 = 16, -2ab = -2X4x(i) = -8i and b^2 = (i)^2 = i^2 = -1 so that
(4-i)^2 =4^2-2X4x(i)+ (i)^2 =16-8i-1