Simiplify : `((1+i)/(1-i))^(4n+1)` (n is a positive integer)

Simiplify : ((1-i)^(3))/((1-i^(3))

(-i)^(4n+3) , where n Is a positive integer.

The least positive integer n such that ((2i)/(1+i))^(n) is a positive integer is

Using De Moivre's theorem, find the least positive integer n such that ((2i)/(1+i))^(n) is a positive integer.

Find the least positive integer n such that ((2i)/(1+i))^n is a positive integer.

Find the least positive integer n such that ((2i)/(1+i))^n is a positive integer.

Find the least positive integer n such that ((2i)/(1+i))^n is a positive integer.

The least positive integer n such that ((2i)/(1+i))^n is a positive integer is a. 16 b. 8 c. 4 d. 2

Statement -1 : The expression ((2i)/(1+i))^(n) is a positive integer for all the values of n. and Statement -2 : Here n=8 is the least positive for which the above expression is a positive integer.

Simiplify : (-(1)/(2)- (sqrt3)/(2)i)^(2)