The conjugate of the complex number (1+i)21−i  is

The given number (1+i)21−i  =  1+i2+2i1−i×  1+i1+i                =  2i(1+i)1−i2    (∵  i2=−1)              =  2i+2i21−(−1)  =  2i+2(−1)2              =i−1  =−1+i. Hence conjugal of the given number is −1−i.