Question

What is the value of -
Square root of -1 multiplied by Square root of -1.

Answer 1

$$\begin{gathered} \mathrm{Consider}\mathrm{the}\mathrm{following}\mathrm{expression}. \\ "\mathrm{Square}\mathrm{root}\mathrm{of}-1\mathrm{multiplied}\mathrm{by}\mathrm{square}\mathrm{root}\mathrm{of}-1" \\ \mathrm{The}\mathrm{corresponding}\mathrm{mathematical}\mathrm{expression}\mathrm{is}, \\ \sqrt{-1}\times \sqrt{-1} \\ \mathrm{Note}\mathrm{that}\mathrm{a}\mathrm{number}"\mathrm{n}"\mathrm{multipled}2\mathrm{times}\mathrm{gives}{\mathrm{n}}^2 \\ \mathrm{So}\mathrm{from}\mathrm{above}\mathrm{it}\mathrm{implies}\mathrm{that}, \\ \sqrt{-1}\times \sqrt{-1}={\left(\sqrt{-1}\right)}^2 \\ \mathrm{Note}\mathrm{that}\sqrt{\mathrm{x}}={\mathrm{x}}^{\frac{1}{2}}\mathrm{which}\mathrm{further}\mathrm{implies}\mathrm{that}, \\ \sqrt{-1}\times \sqrt{-1}={\left({\left(-1\right)}^{1/2}\right)}^2 \\ ={\left(-1\right)}^{\frac{1}{2}\times 2} \\ ={\left(-1\right)}^1 \\ =\mathbf{-}\mathbf{1} \end{gathered}$$