Let` z= a+ ib` (where` a,b,in R` and` i = sqrt(-1)` such that `|2z+3i| = |z^(2)` identify the correct statement(s)?

Let z=a+ib=re^(i theta) where a, b, theta in R and i=sqrt(-1) Then r=sqrt((a^(2)+b^(2)))=|Z| and theta=tan^(-1)((b)/(a))=arg(z) Now |z|^(2)=a^(2)+b^(2)=(a+ib)(a-ib)=zbar(z) rArr(1)/(2)=(bar(z))/(|z|^(2)) and |z_(1)z_(2)z_(3)......z_(n)|=|z_(1)||z_(2)||z_(3)|...|z_(n)| If |f(z)|=1 ,then f(z) is called unimodular. In this case f(z) can always be expressed as f(z)=e^(i alpha), alpha in R Also e^(i alpha)+e^(i beta)=e^(i((alpha+beta)/(2)))*2cos((alpha-beta)/(2)) and e^(i alpha)-e^(i beta)=e^(i((alpha+beta)/(2)))*2i sin((alpha-beta)/(2)) where alpha, beta in R Q:If Z_(1),Z_(2),Z_(3) are complex number such that |Z_(1)|=|Z_(2)|=|Z_(3)|=|Z_(1)+Z_(2)+Z_(3)|=1 , then |(1)/(Z_(1))+(1)/(Z_(2))+(1)/(Z_(3))| is

Let z be a complex number on the locus (z-i)/(z+i)=e^(i theta)(theta in R) , such that |z-3-2i|+|z+1-3i| is minimum. Then,which of the following statement(s) is (are) correct?

Let z = x + iy be a non - zero complex number such that z^(2) = I |z|^(2) , where I = sqrt(-1) then z lies on the :

If z=i^(i) where i=sqrt(-)1 then |z| is equal to