Question

x² + 1 = 0

Answer 1

Given: 

\[x^2 + 1 = 0\]

\[x^2 + 1 = 0\]

\[ \Rightarrow x^2 - 1 i^2 = 0\]

\[ \Rightarrow (x + i) (x - i) = 0 [ ( a^2 - b^2 ) = (a + b) (a - b)]\]

\[\Rightarrow (x + i) = 0\] or \[(x - i) = 0\]

\[\Rightarrow x = - i\]  or  \[x = i\]

Hence, the roots of the equation are  \[i \text { and }- i\].