Question

Imagine writing π9i = 6 i(i²) (i − 1) · (i + 1) in extended form. What factor corresponds to i = 6? What factor corresponds to i = 9?

a) i + 1
b) i - 1
c) i²
d) i³

Answer 1

The question incorrectly associates factors with specific integer values of 'i'. The factors given, such as I + 1, I - 1, i², and i³, do not correspond to i equals 6 or 9. Instead, i² is associated with i = 6 because it results in a real number when i is squared.

Step-by-step explanation:

The question is asking to identify which factor would correspond to I am equaling 6 and 9 in the expression π9i = 6 I(i²) (I − 1) · (I + 1). Firstly, we need to recognize that when I am raised to an even power, the result is a real number, and when raised to an odd power, the result is an imaginary number. So, i², which is I squared, is a factor corresponding to i = 6, because i² = -1 and 6(-1) is a real number. As for i¹, or I to the first power, it would correspond to i = 9, because it remains an imaginary unit.

Therefore, in the context of the given expression, there is no direct 'factor' for I = 6 or I = 9, but rather i² and I in general represent the behaviors at those powers. The choices provided, a) I + 1 b) I - 1 c) i² d) i³, are just expressions involving I and do not explicitly correspond to I = 6 or I = 9.

Answer 2

The factor corresponding to i=6 is 7560 and the factor corresponding to i=9 is 38880.

Step-by-step explanation:

In the given expression, π9i = 6 i(i²) (i − 1) · (i + 1), we need to determine which factor corresponds to i = 6 and i = 9.

When i = 6, substitute this value into the expression:

π9(6) = 6(6²)(6 − 1)(6 + 1) = 6(36)(5)(7) = 7560.

So, the factor corresponding to i = 6 is 7560.

Similarly, when i = 9, substitute this value into the expression:

π9(9) = 6(9²)(9 − 1)(9 + 1) = 6(81)(8)(10) = 38880.

Therefore, the factor corresponding to i = 9 is 38880.

In the provided expression, π9i = 6 i(i²) (i − 1) · (i + 1), the goal is to determine the values corresponding to i = 6 and i = 9. For i = 6, substitution yields π9(6) = 6(6²)(6 − 1)(6 + 1) = 6(36)(5)(7) = 7560. Consequently, the factor associated with i = 6 is 7560. Similarly, for i = 9, substitution results in π9(9) = 6(9²)(9 − 1)(9 + 1) = 6(81)(8)(10) = 38880.

Hence, the factor corresponding to i = 9 is 38880. These values represent the outcomes of the given expression for the specified values of i. The process involves substituting the respective values, performing the calculations, and identifying the factors corresponding to each value of i, demonstrating the practical application of algebraic evaluation for specific inputs in the given expression.