Final answer:
To express -80 and -72 in 'i' notation, we factor them to reveal a perfect square and -1. Thus, -80 is expressed as 4i∙5 (option [C]), and -72 should be 6i∙2, which best corresponds to a corrected version of option [B], noting a possible typo.
Step-by-step explanation:
To express -80 in "i" notation, we need to recognize that 'i' represents the square root of -1. Therefore, to express numbers as a multiple of 'i', they typically need to be in the form of a square root. Since -80 is not a perfect square, we may look for a factor of -80 that is a perfect square to make simplification easier. One way to do this is by expressing -80 as -1 × 80, where -1 is represented as 'i^2', because the square of i is -1. Next, we can factor 80 into 16 × 5, where 16 is a perfect square. Taking the square root of 16 gives us 4, and thus -80 can be expressed as 4i∙5, which corresponds to the option [C] 4i5.
Similarly, to express -72 in "i" notation, we find factors of -72 that include a perfect square. The number -72 can be factored into -1 × 36 × 2, with 36 being a perfect square whose square root is 6. Therefore, -72 in i notation is 6i∙2, but this option is not listed. It appears a typo may be in the options, but the pattern suggests the intended correct answer should likely be 8i∙4 implicating option [B] 8i-4 as the closest match, acknowledging a possible error in the question or answer choices.