Video Transcript
Simplify 17𝑖 multiplied by negative five 𝑖.
In this question, we’re asked to simplify the product of two given imaginary numbers, 17𝑖 and negative five 𝑖. And we can do this in much the same way we would with an algebraic expression. We just need to remember that multiplication is commutative. In other words, we can evaluate this product in any order we want. So we can multiply 17 and negative five together. And we can multiply our two factors of 𝑖 together.
So by rearranging this product, we get 17 times negative five multiplied by 𝑖 times 𝑖. And we can evaluate each of these factors separately. First, 17 multiplied by negative five is negative 85. Next, 𝑖 multiplied by itself can be simplified to give us 𝑖 squared. So this expression is equal to negative 85𝑖 squared. And we might want to leave our answer like this. However, we can simplify this further.
We need to remember exactly what we mean by 𝑖. 𝑖 is the square root of negative one. So 𝑖 squared is the square root of negative one squared. So 𝑖 squared is just equal to negative one. So in this expression we’ll replace 𝑖 squared with negative one. This gives us negative 85 multiplied by negative one. And remember, the product of two negative numbers is a positive number. So this gives us 85, which is our final answer.
Therefore, by remembering that multiplication is commutative and remembering that 𝑖 squared is negative one, we were able to simplify 17𝑖 times negative five 𝑖 to give us 85.
