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−1⋅−1\sqrt{-1} \cdot \sqrt{-1}

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Full solution

Q. −1⋅−1\sqrt{-1} \cdot \sqrt{-1}
  1. Apply definition of imaginary unit: We have: −1×−1\sqrt{-1} \times \sqrt{-1}\newlineApply the definition of the imaginary unit.\newlineThe square root of −1-1 is defined as the imaginary unit ii.\newlineSo, −1×−1=i×i\sqrt{-1} \times \sqrt{-1} = i \times i
  2. Multiply imaginary units: Multiply the imaginary units. i×i=i2i \times i = i^2
  3. Apply definition of ii squared: Apply the definition of ii squared.\newlineBy definition, i2=−1i^2 = -1.\newlineSo, i×i=i2=−1i \times i = i^2 = -1

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