JEE Main20248 Apr 2024Evening ShiftMathematicsComplex NumberActual

The sum of all possible values of [- , 2 ] , for which 1+i 1-2 i is purely imaginary, is equal

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Correct answer

A. 3

Step-by-step solution

aligned & Z= 1+i 1-2 i & Z=- Z 1+i 1-2 i =- ( 1+i 1-2 i ) & (1+i )( 1-2 i )=-(1-2 i )( 1+i ) & (1+i )(1+2 i )=-(1-2 i )(1-i ) & 1+3 i -2 ^2 =- (1-3 i -2 ^2 ) & 2-4 ^2 =0 & ^2 = 1 2 =- 4 ,- 3 4 , 4 , 3 4 , 5 4 , 7 4 & sum =3 aligned

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