If `z = sqrt(3)+i`, find |z| and Arg(z).

If z = (sqrt(3+i))/2 (where i = sqrt(-1) ) then (z^101 + i^103)^105 is equal to

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

If z= sqrt3+i , then the argument of z^2 e^(z-i) is equal to :

If z_1 = 2 -i and z_2= -2+i , find Re((z_1 z_2)/z_1) .

Let Papoint denoting a comples number z on the complex plane. i.e." "z=Re(z)+i Im(z)," where "i=sqrt(-1) if" "Re(z)=xand Im (z)=y,then z=x+iy If Pmovew such that |Re(z)|+|Im(z)=a(ainR^(+)) The locus of P is

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then z 1 ​ +z 2 ​ 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

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=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Find the value of Im(z) .