A real value of x will satisfy the equation 3 - 4 i x 3 + 4 i x = α - i β ( α , β a r e r e a l ) , if

Step-by-step solution

Given, α - i β = 3 + i ( - 4 x ) 3 + i ( 4 x ) ⇒ α + i - β = 3 + i ( - 4 x ) 3 + i ( 4 x ) ⇒ α + i - β = | 3 + i ( - 4 x ) | | 3 + i ( 4 x ) | ⇒ α 2 + β 2 = 3 2 + - 4 x 2 3 2 + 4 x 2 ⇒ α 2 + β 2 = 9 + 16 x 2 9 + 16 x 2   ⇒ α 2 + β 2 = 1