Final answer:
The correct answer to the given complex expression is option D) 14 + 18i, which is found by replacing i^2 with -1 and simplifying the equation.
Step-by-step explanation:
The question asks to find which of the provided complex numbers is equal to the expression (5 + 12i) - (9i^2 - 6i), where i is the imaginary unit, equal to the square root of -1. To solve for this, we must remember that i^2 = -1, which changes the expression to (5 + 12i) - (-9 - 6i). Simplifying this, we combine like terms to get the final answer which is 14 + 18i.
The steps to solve the expression are as follows:
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- Replace i^2 with -1 to get rid of the imaginary unit's square.
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- Simplify the expression by combining real parts and imaginary parts separately.
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- Write down the simplified form of the complex number.
Therefore, the correct option from the given alternatives is option D) 14 + 18i.