What is the value of the expression i^0 + i^1 + i^2 + i^3 + i^4?

The expression i⁰ + i¹ + i² + i³ + i⁴ involves the imaginary unit i, which is defined as the square root of -1. To evaluate this expression, we will calculate each power of i and then sum them up.

Let’s break it down:

• i⁰ = 1 (Any number to the power of zero is 1)
• i¹ = i
• i² = -1 (Since i is the square root of -1)
• i³ = i² * i = -1 * i = -i
• i⁴ = (i²)² = (-1)² = 1

Now, substituting these values back into the expression gives us:

1 + i – 1 – i + 1

When we simplify this sum:

• 1 – 1 + 1 = 1
• i – i = 0

Combining these results, we find:

Value of the expression = 1

Therefore, the value of the expression i⁰ + i¹ + i² + i³ + i⁴ is 1.