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 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 :

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew

Let z and w be two complex numbers such that |z|le1, |w|le1 and |z-iw|=|z-i bar w|=2 , then z equals :

If z_1a n dz_2 are two nonzero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to

If z_1=a + ib and z_2 = c + id are complex numbers such that |z_1|=|z_2|=1 and Re(z_1 bar z_2)=0 , then the pair of complex numbers omega_1=a+ic and omega_2=b+id satisfies a. |omega_(1)|=1 b. |omega_(2)|=1 c. Re(omega_(1)baromega_(2))=0 d. None of these

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

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

Let alpha and beta be two fixed non-zero complex numbers and 'z' a variable complex number. If the lines alphabarz+baraz+1=0 and betabarz+barbetaz-1=0 are mutually perpendicular, then

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(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))