Question

Evaluate: (—3 + 10.5) divided by (—1.5+3 2)
A: —1
B: 1
C: — 7 2/3
D: 1 2/3

Answer 1

First, let's simplify the expression inside the brackets:

(-1.5 + 3i) = (-1.5 + 3i) / 1

To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator:

(-1.5 + 3i) / 1 = (-1.5 + 3i) * (1.5 - 3i) / (1 * (1.5 - 3i))

Simplifying the numerator:
(-1.5 + 3i) * (1.5 - 3i) = -1.5 * 1.5 + 3i * 1.5 + (-1.5) * (-3i) + 3i * (-3i) = 2.25 + 4.5i + 4.5i + 9i^2 = 2.25 + 9i^2

Since i^2 = -1, we can substitute and simplify further:
2.25 + 9i^2 = 2.25 + 9 * (-1) = 2.25 - 9 = -6.75

Now, we can rewrite the expression as:
(-3 + 10.5) / (-6.75) = 7.5 / (-6.75)

Dividing 7.5 by -6.75:
7.5 / (-6.75) = -1.111...

Rounding off to one decimal place, the result is approximately -1.1.

Therefore, the correct answer is not listed among the given options.