Final answer:
The equivalent complex number to the expression (2 + i)(8 - 3i) - (23 + 34i) through multiplication and subtraction is -4 - 32i, which is not listed in the given options.
Step-by-step explanation:
To find which complex number is equivalent to the given expression (2 + i)(8 - 3i) - (23 + 34i), we need to perform the multiplication and subtraction.
Step 1: Multiply the complex numbers (2 + i) and (8 - 3i).
(2 + i)(8 - 3i) = 16 - 6i + 8i - 3i2
Since i2 = -1, let's replace that.
(2 + i)(8 - 3i) = 16 - 6i + 8i + 3 = 19 + 2i
Step 2: Subtract (23 + 34i) from the result obtained in Step 1.
19 + 2i - (23 + 34i) = 19 + 2i - 23 - 34i
Step 3: Combine like terms (real with real and imaginary with imaginary).
19 - 23 + 2i - 34i = -4 - 32i
The equivalent complex number is -4 - 32i, which is not an option provided in the question. Therefore, there might be a mistake in the provided options or in the calculation.