QuestionAugust 26, 2025

If i=sqrt (-1) what is i^4 equal to? Explain or show the work that leads to your answer. Edit View Insert Format Tools Table square

If i=sqrt (-1) what is i^4 equal to? Explain or show the work that leads to your answer. Edit View Insert Format Tools Table square
If i=sqrt (-1) what is i^4 equal to?
Explain or show the work that leads to your answer.
Edit View Insert Format Tools Table
square

Solution
3.6(239 votes)

Answer

1 Explanation 1. Understand the property of i The imaginary unit i is defined as i = \sqrt{-1}, and it follows that i^2 = -1. 2. Calculate higher powers of i Using i^2 = -1, we find i^3 = i^2 \cdot i = -1 \cdot i = -i. Then, i^4 = i^3 \cdot i = (-i) \cdot i = -i^2 = -(-1) = 1.

Explanation

1. Understand the property of $i$<br /> The imaginary unit $i$ is defined as $i = \sqrt{-1}$, and it follows that $i^2 = -1$.<br />2. Calculate higher powers of $i$<br /> Using $i^2 = -1$, we find $i^3 = i^2 \cdot i = -1 \cdot i = -i$.<br /> Then, $i^4 = i^3 \cdot i = (-i) \cdot i = -i^2 = -(-1) = 1$.
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