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What is the value of z if z^2 = -1?

Practice Questions

Q1
What is the value of z if z^2 = -1?
  1. i
  2. -i
  3. 1
  4. 0

Questions & Step-by-Step Solutions

What is the value of z if z^2 = -1?
  • Step 1: Understand the equation z^2 = -1. This means we are looking for a number z that, when multiplied by itself (squared), equals -1.
  • Step 2: Realize that no real number squared gives a negative result. For example, 2^2 = 4 and (-2)^2 = 4, both are positive.
  • Step 3: Introduce the concept of imaginary numbers. The imaginary unit is denoted as 'i', where i is defined as the square root of -1.
  • Step 4: Rewrite the equation using the imaginary unit. Since i^2 = -1, we can say z = i or z = -i.
  • Step 5: Conclude that the solutions to the equation z^2 = -1 are z = i and z = -i.
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