Question

Find the value of the expression given below (8 - 3i) - (8 - 3i)(8 + 8i)

Answer 1

$(8-3i)-(8-3i)(8+8i)=(8-3i)[1-(8+8i)]\\\\=(8-3i)(1-8-8i)=(8-3i)(-7-8i)\\\\=(8)(-7)+(8)(-8i)-(3i)(-7)-(3i)(-8i)\\\\=-56-64i+21i+24i^2=-56-43i+24(-1)\\\\=-56-43i-24=-80-43i\\\\\\i=\sqrt{-1}\to i^2=-1$

Answer 2

Follow PEMDAS. First is multiplication.

Follow the FOIL method: (First, Outside, Inside, Last)
(8 - 3i) - (8 - 3i)(8 + 8i)
8(8) = 64
8(8i) = 64i
-3i(8) = -24i
-3i(8i) = 24   (note: two "i"'s = -1)

Combine like terms

64 + 64i - 24i + 24

64 + 40i + 24

88 + 40i

Now subtract 88 + 40i from 8 - 3i

(8 - 3i) - (88 + 40i) = -80 - 43i (Note: the signs in the parenthesis change,                                                          because you are subtracting as a whole)

-80 - 43i is your answer


hope this helps