if A = -3 + 5i, B = 4 - 2i, and C = 1 +6i, where i is the imaginary unit, then A - BC equals 1) 5 - 17i 2) 5 + 27i 3) -19 - 17i 4) -19 + 27i
Mathematics · Middle School · Thu Feb 04 2021
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First, we should compute the product of B and C.
B = 4 - 2i C = 1 + 6i
BC = (4 - 2i)(1 + 6i)
To perform the multiplication, we apply the distributive property, also known as the FOIL method in algebra for binomials:
BC = 4(1) + 4(6i) - 2i(1) - 2i(6i) BC = 4 + 24i - 2i - 12i^2
Since i^2 = -1 (by the definition of the imaginary unit i), we can substitute -1 for i^2:
BC = 4 + 24i - 2i + 12 BC = (4 + 12) + (24i - 2i) BC = 16 + 22i
Now that we have the value for BC, we can compute A - BC:
A = -3 + 5i BC = 16 + 22i
A - BC = (-3 + 5i) - (16 + 22i) A - BC = -3 + 5i - 16 - 22i A - BC = -3 - 16 + 5i - 22i A - BC = -19 - 17i
Therefore, the correct answer is 3) -19 - 17i.