Which of the following is equivalent to −3i(4i+5i)%0D%0A−%0D%0A3%0D%0A𝑖%0D%0A(%0D%0A4%0D%0A𝑖%0D%0A+%0D%0A5%0D%0A𝑖%0D%0A)%0D%0A ?(1 point)%0D%0AResponses%0D%0A%0D%0A12+15i%0D%0A12%0D%0A+%0D%0A15%0D%0A𝑖%0D%0A12 plus 15 i%0D%0A%0D%0A27%0D%0A27%0D%0A27%0D%0A%0D%0A27i%0D%0A27%0D%0A𝑖%0D%0A27 i%0D%0A%0D%0A−27

Question

Which of the following is equivalent to  −3i(4i+5i)%0D%0A−%0D%0A3%0D%0A𝑖%0D%0A(%0D%0A4%0D%0A𝑖%0D%0A+%0D%0A5%0D%0A𝑖%0D%0A)%0D%0A ?(1 point)%0D%0AResponses%0D%0A%0D%0A12+15i%0D%0A12%0D%0A+%0D%0A15%0D%0A𝑖%0D%0A12 plus 15 i%0D%0A%0D%0A27%0D%0A27%0D%0A27%0D%0A%0D%0A27i%0D%0A27%0D%0A𝑖%0D%0A27 i%0D%0A%0D%0A−27

GPT-4o mini · Answer

To simplify $ -3i(4i + 5i) $, we start by combining the terms inside the parentheses: $$ 4i + 5i = 9i $$ Now, substituting this back into the expression, we have: $$ -3i(9i) $$ Next, we can multiply these two terms: $$ -3i \cdot 9i = -27i^2 $$ Recall that $ i^2 = -1 $. Thus: $$ -27i^2 = -27(-1) = 27 $$ So the expression simplifies to: $$ 27 $$ Therefore, the answer is $ \boxed{27} $.