In mathematics, "i" is the imaginary unit, which is defined as:

$i = \sqrt{-1}$

It is used to extend the number system beyond real numbers, forming the set of complex numbers. Complex numbers have the form:

$a + bi$

where:

• $a$ is the real part
• $b$ is the imaginary part

Some key properties of $i$:

1. $i^2 = -1$
2. $i^3 = -i$
3. $i^4 = 1$
4. The powers of $i$ repeat every 4 cycles: $i, -1, -i, 1$.

Would you like a more detailed explanation or examples?

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Related Questions:

1. What are complex numbers and how are they used?
2. How do you perform arithmetic operations with imaginary numbers?
3. What is the geometric interpretation of $i$ in the complex plane?
4. How do imaginary numbers appear in real-world applications?
5. How do you solve equations using imaginary numbers?

Tip: When solving quadratic equations, if the discriminant $b^2 - 4ac$ is negative, the solutions involve imaginary numbers!