`((1+i)^(4n +5))/((1+i)^(4n + 5))` किसके बराबर है, जहाँ n एक धन पूर्णांक है और `i =sqrt(-1)` है?

1 + i^(2n) + i^(4n) + i^(6n)

What is ((1+i)^(4n+5))/((1-i)^(4n+3)) equal to, where n is a natural number and i=sqrt(-1) ?

Evaluate (i^(4n+1) - i^(4n-1)) .

Evaluate : (i) i^(135) (ii) i^((1)/(47) (iii) (-sqrt(-1))^(4n +3) , n in N (iv) sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9)

Evaluate : (i) i^(135) (ii) i^(-47) (iii) (-sqrt(-1))^(4n +3) , n in N (iv) sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9)

For positive integers n_(1), n_(2) the value of the expression (1+i)^(n_(1)) + (1+ i^(3))^(n_(1)) + (1+ i^(5))^(n_(2)) + (1+ i^(7))^(n_(2)) , where i= sqrt-1 is a real number if and only if

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i^5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :