All the points in the set `S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt(-1))lie` on a

If S={(alpha+i)/(alpha-i),alpha in R} then the S lies on

Let S = {(2alpha+3i)/(2alpha-3i):alpha in R} . All the points of S lie on a circle of radius ____________.

Show that the point (x,y), where : x=a+r cos alpha, y=b+r sin alpha lie on a circle for all values of alpha .

If alpha=cos theta+i sin theta, then (1+alpha)/(1-alpha) equals ( (i)cot theta(ii)i tan((theta)/(2))(iii)i cot((theta)/(2))(iv)cot((theta)/(2))

If z = ((1+i)^(2))/(alpha-i) , alpha in R has magnitude sqrt((2)/(5)) then the value of alpha is (i) 3 only (ii) -3 only (iii) 3 or -3 (iv) none of these

For a complex number z the minimum value of |z|+|z-cos alpha-i sin alpha| (where i=sqrt(-1)) is:

A sample space consists of 4 elements S=(alpha_(1), alpha_(2), alpha_(3), alpha_(4)) Which defines a probability function on S (where" "alpha_(i)capalpha_(j)nephi" "AA" "i nejand cupalpha_(i)=S)

If alpha and beta are the complex roots of the equation (1+i)x^(2)+(1-i)x-2i=0 where i=sqrt(-1) , the value of |alpha-beta|^(2) is