Solve `( sin x + "i" cos x )/( 1 +i),i =sqrt(-1)` when it is purely imaginary .

The value of x in[-2pi,2pi] such that (sinx+icosx)/(1+i),i=sqrt(-1) , is purely imaginary ,are given by

If (1+i cos theta)/(1-2i cos theta) is purely imaginary then theta =

Find the least positive integral value of n, for which ((1-i)/(1+i))^n , where i=sqrt(-1), is purely imaginary with positive imaginary part.

Find the least positive integral value of n, for which ((1-i)/(1+i))^n , where i=sqrt(-1), is purely imaginary with positive imaginary part.

Find the least positive integral value of n, for which ((1-i)/(1+i))^n , where i=sqrt(-1), is purely imaginary with positive imaginary part.

Find the real values of theta , such that (3 + 2i sin theta)/(1 - 2i sin theta) is purely Imaginary

Show that ( 2 + i sqrt(3))^(10) - (2 - i sqrt(3))^(10) is purely imaginary.

Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is purely imaginary } Then the sum of the elements in A is