Let z be a non-real complex number
lying on `|z|=1,` prove that `z=(1+itan((arg(z))/2))/(1-itan((arg(z))/(2)))` (where `i=sqrt(-1).)`

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

Let z and w be two non-zero complex numbers such that ∣z∣=∣w∣ and arg(z)+arg(w)=π, then z equals

If |z-1|=1, where z is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).

Given that |z-1|=1, where z is a point on the argand planne , show that (z-2)/(z)=itan (arg z), where i=sqrt(-1).

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

If z and w are two non-zero complex numbers such that |zw|=1 and Arg (z) -Arg (w) =pi/2 , then bar z w is equal to :

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1 z_2|= |z_1||z_2| .

For any two complex numbers z_1 and z_2 , prove that Re (z_1 z_2) = Re z_1 Re z_2 - Imz_1 Imz_2

Let z_(1) and z_(2) be two distinct complex numbers and z=(1-t)z_(1)+tz_(2) , for some real number t with 0 lt t lt 1 and i=sqrt(-1) . If arg(w) denotes the principal argument of a non-zero complex number w, then a. abs(z-z_(1))+abs(z-z_(2))=abs(z_(1)-z_(2)) b. arg(z-z_(1))=arg(z-z_(2)) c. |{:(z-z_(1),bar(z)-bar(z)_(1)),(z_(2)-z_(1),bar(z)_(2)-bar(z)_(1)):}|=0 d. arg(z-z_(1))=arg(z_(2)-z_(1))