To solve the quadratic equation \( x^2 + 1 = 0 \), we need to find the values of \( x \) that satisfy the equation.

1. Start by isolating \( x^2 \):
   \[
   x^2 = -1
   \]

2. To solve for \( x \), take the square root of both sides. Remember that taking the square root of a negative number involves imaginary numbers:
   \[
   x = \pm \sqrt{-1}
   \]

3. By definition, \( \sqrt{-1} = i \) (where \( i \) is the imaginary unit):
   \[
   x = \pm i
   \]

Therefore, the solutions to the equation \( x^2 + 1 = 0 \) are:
\[
x = i \quad \text{and} \quad x = -i
\]

Would you like further details or have any questions?

Here are some questions you might consider next:
1. What are complex numbers and how are they represented?
2. How do you add, subtract, multiply, and divide complex numbers?
3. What are the properties of the imaginary unit \( i \)?
4. How do you graph complex numbers on the complex plane?
5. What are some applications of complex numbers in engineering and physics?

**Tip:** When solving quadratic equations, if the discriminant is negative, the solutions will involve imaginary numbers, indicating that the roots are complex.

Learn how to solve the quadratic equation x^2 + 1 = 0 involving complex solutions. Understand the use of the imaginary unit (i) in mathematics and its application in quadratic equations. Suitable for students in Grades 10-12.

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