KCET2024MathematicsComplex Number
The real value of ' ' for which 1-i 1+2 i is purely real is
Options
- A(n+1) 2 , n N
- B(2 n+1) 2 , n N
- Cn , n N
- D(2 n-1) 2 , n N
Correct answer
C. n , n N
Step-by-step solution
Given, 1-i 1+2^j is purely real i.e. 1-i 1+2 i (1-2 i ) (1-2 i ) = 1-i -2 i +2 i^2 ^2 1-4 i^2 ^2 = 1-3 i -2 ^2 1+4 ^2 = 1-2 ^2 1+4 ^2 +i ( -3 1+4 ^2 ) which is given to purely real -3 1+4 ^2 =0 -3 =0 =0 Hence, =n , n N