Question

Which of the following is equivalent to 5i^16 + 3i^23 + i^26?

8 + 2i
5 - 4i
2 + 7i
4 - 3i

Answer 1

To simplify the expression, we can use the definition of the imaginary unit i to evaluate each term and then combine them.

Step-by-step explanation:

To find the equivalent expression, we need to simplify each term and then combine them together. We know that i is defined as the imaginary unit, where i^2 = -1. Using this information, we can simplify each term:

5i^16 = 5(-1)^8 = 5(1) = 5

3i^23 = 3(-1)^11 = 3(-1) = -3

i^26 = (-1)^13 = -1

Now we can combine the simplified terms:

5i^16 + 3i^23 + i^26 = 5 + (-3) + (-1) = 1

Therefore, the equivalent expression is 1.