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What is the solution set of the equation x^2 + 1 = 0?

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Question: What is the solution set of the equation x^2 + 1 = 0?

Options:

  1. {0}
  2. {±i}
  3. {1}
  4. {-1}

Correct Answer: {±i}

Solution: 

The equation has no real solutions; the solutions are x = i and x = -i.

What is the solution set of the equation x^2 + 1 = 0?

Practice Questions

Q1
What is the solution set of the equation x^2 + 1 = 0?
  1. {0}
  2. {±i}
  3. {1}
  4. {-1}

Questions & Step-by-Step Solutions

What is the solution set of the equation x^2 + 1 = 0?
  • Step 1: Start with the equation x^2 + 1 = 0.
  • Step 2: Move 1 to the other side of the equation by subtracting 1 from both sides. This gives us x^2 = -1.
  • Step 3: To solve for x, we need to take the square root of both sides. The square root of -1 is not a real number.
  • Step 4: Instead, we use the imaginary unit 'i', where i = √(-1). So, the square root of -1 is i.
  • Step 5: Therefore, we have two solutions: x = i and x = -i.
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