If , then find the least positive integral value of m .
It is given that,
( 1 + i 1 − i ) m = 1
Rationalize the denominator,
( 1 + i 1 − i × 1 + i 1 + i ) m = 1 ( ( 1 + i ) 2 1 2 − i 2 ) m = 1 ( 1 + i 2 + 2 i 1 + 1 ) m = 1 ( 1 − 1 + 2 i 2 ) m = 1
Simplify further,
( i ) m = ( i ) 4 m = 4
Therefore, the least integral value of m is 4.
It is given that,
Rationalize the denominator,
Simplify further,
Therefore, the least integral value of
