`arg(1/barz)=arg((zbarz)/(barz))`

Fill in the blanks of the following arg(z)+ arg(barz) where (barz ne 0) is.....

if z_1=1+isqrt3 , z_2=sqrt3-i show that (a)arg (z_1z_2)=arg(z_1)+arg(z_2) and (b) arg(z_1//z_2)=arg(z_1)-arg(z_2)

arg(z) + arg(barz) (z != 0) is ………..

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)

Show that the equation of the circle in the complex plane with z_1 & z_2 as its diameter can be expressed as , 2z barz-(barz_1+barz_2)z-(barz_1+barz_2)barz+z_1barz_2+z_2barz_1=0

Conjugate of a complex no and its properties. If z, z_1, z_2 are complex no.; then :- (i) bar(barz)=z (ii)z+barz=2Re(z)(iii)z-barz=2i Im(z) (iv)z=barz hArr z is purely real (v) z+barz=0implies z is purely imaginary (vi)zbarz=[Re(z)]^2+[Im(z)]^2

Let z be a unimodular complex number. Statement-1:arg (z^(2)+barz)="arg"(z) Statement-2:barz= cos("arg"z)-isin("arg"z)

Let z be a unimodular complex number. Statement-1:arg (z^(2)+barz)="arg"(z) Statement-2:barz= cos("arg"z)-isin("arg"z)