If x 4 + 2 x i - 3 x 2 + y i = 3 - 5 i + 1 + 2 y i , then the number of ordered pairs x , y is/are equal to ∀ x , y ∈ R  a n d  i 2 = - 1

Step-by-step solution

x 4 - 3 x 2 - 3 - 1 = 0 & 2 x - y + 5 - 2 y = 0 x 2 - 4 x 2 + 1 = 0 & 2 x - 3 y + 5 = 0 ⇒ x = 2   or   - 2 & 2 x - 3 y + 5 = 0 When x = 2 , y = 3 and when x = - 2 , y = 1 3 ⇒ x , y = 2,3   &   - 2 , 1 3 ⇒ Number of ordered pair of x , y is equal to 2