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

Question

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, α 2 - β 2 = - 1, α 2 - β 2 = 1, α 2 + β 2 = 1, α 2 - β 2 = 2

MARKS App · Accepted Answer

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

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