Homework SourseVerify whether Ln1 i2 2Ln1 i is correct or not Here Ln me
Verify whether Ln((-1 + i)^2) = 2Ln(-1 + i) is correct or not. [Here Ln means Principal logarithm]![Verify whether Ln((-1 + i)^2) = 2Ln(-1 + i) is correct or not. [Here Ln means Principal logarithm]SolutionLn( (-1 + i)2 ) = Ln( (-1)2 + 2.(-1).i + (i)2 ) [ Sin](/WebImages/36/verify-whether-ln1-i2-2ln1-i-is-correct-or-not-here-ln-me-1109350-1761587824-0.webp "Verify whether Ln((-1 + i)^2) = 2Ln(-1 + i) is correct or not. [Here Ln means Principal logarithm]SolutionLn( (-1 + i)2 ) = Ln( (-1)2 + 2.(-1).i + (i)2 ) [ Sin")
Solution
Ln( (-1 + i)2 ) = Ln( (-1)2 + 2.(-1).i + (i)2 ) [ Since , (a + b)2 = a2 + 2ab + b2 ]
= Ln( 1 - 2i + i2 )
= Ln( 1 - 2i + (-1) ) [ Since , i2 = -1 ]
Ln( (-1 + i)2 ) = Ln( -2i )
Hence ,
Ln( (-1 + i)2 ) = 2Ln(-1 + i) is not correct
