Question

Consider the complex number i . select all numbers equivalent to − 1 . a.consider the function f ( x ) = 2 x 3 5 . Which expression is the inveconsider the function f ( x ) = 2 x 3 5 . which expression is the inverse of f ( x ) ?rse of f ( x ) ? i b. − i c. i 2 d. − i 2 e. i 4 f. i 150 g. i 800

Answer 1

The correct selections for numbers equivalent to -1 using powers of i are i squared (i^2). The pattern of i's powers (i, -1, -i, 1) repeats every four powers, so no other options provided are equivalent to -1.

Step-by-step explanation:

The complex number i represents the square root of -1. To find numbers equivalent to -1 using powers of i, recall the pattern of powers of i: i, -1, -i, 1, and then it repeats. Thus, i to the fourth power (i4) equals 1, and every fourth power of i beyond that is also 1, making i to the 150th or 800th power equivalent to i4. Since i2 equals -1, the numbers equivalent to -1 are i2 (c) and i to any even power, which is not listed as an option besides i2. So the correct selections are i2 (c) and not any of the other choices provided.