Answer:
3) -19 - 17i is our answer
Step-by-step explanation:
to solve A - BC we plug in the values given
A= -3 + 5i
B = 4 - 2i
C = 1 + 6i
-3 + 51i - (4 - 2i)(1 + 6i) is our expression. we can FOIL (4 - 2i)(1 + 6i) this expression out. FOIL stands for:
First
Outside
Inside
Last
i will highlight the terms i am using in the current step in bold and put the result next of those two terms next to the expression
F: (4 - 2i)(1 + 6i) = 4
O: (4 - 2i)(1 + 6i) = 24i
I: (4 - 2i)(1 + 6i) = -2i
L: (4 - 2i)(1 + 6i) = 12 < --- the reason why its 12 and not -12i or 12i is because i = √-1 and i² = -1
when we multiply -2i * 6i, we would have gotten a -12i², and i² = -1, so we are multiplying -12 by -1, which gives us 12 as the result
combining all these terms together and we have:
4 + 24i - 2i + 12
in the expression this is:
-3 + 5i - (4 + 24i - 2i + 12) < we need to distribute the negative sign into (4 + 24i - 2i + 12) and we now get:
-3 + 5i -4 - 24i + 2i - 12 < combine like terms (ex: i terms together)
-3 - 4 - 12 = -19
5i - 24i + 2i = -17i
the result of the expression is:
-19 - 17i
we cannot simplify this any further so this is our answer. the answer choice that matches this is 3, so 3) -19 - 17i is our answer
The result of the expression where i is the imaginary unit is -19-17i. Option 3 is correct
Given the following complex numbers A = -3 + 5i, B = 4 - 2i, and C = 1 +6i
We need to solve for A - BC
BC = (4 - 2i)(1 + 6i)
BC = 4(1) + 4(6i) - 2i(1) - 2i(6i)
BC = 4 + 24i -2i - 12(-1)
BC = 16+22i
Evaluate A - BC
A - BC = (-3 + 5i) - (16 + 22i)
A - BC = -3-16 + 5i - 22i
A - BC = -19 - 17i
Hence the result of the expression where i is the imaginary unit is -19-17i
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