The least positive integer n such that ( 2 i ) n ( 1 - i ) n - 2 , i = - 1 , is a positive integer, is ______.

Question

The least positive integer n such that ( 2 i ) n ( 1 - i ) n - 2 , i = - 1 , is a positive integer, is ______.,

MARKS App · Accepted Answer

( 2 i ) n ( 1 - i ) n - 2 = ( 2 i ) n ( - 2 i ) n - 2 2 = ( 2 i ) n + 2 2 ( - 1 ) n - 2 2 = 2 n + 2 2 i n + 2 2 ( - 1 ) n - 2 2 Clearly n must be even n = 2 , 4 rejected. So the least positive integer possible is n = 6

Search any question & find its solution

Looking for more such questions to practice?