Let `z=log_(2)(1+i)` then `(z+bar(z))+i(z-bar(z))=`

If z=i-1, then bar(z)=

If z_(1) = 3+4i and z_(2) = 2+i , and z satisfy the equation 2(z+bar(z)) + 3(z-bar(z))i = 0 , Then for Minimum value of |z-z_(1)| + |z-z_(2)| , possible value of z can be

If z_1 and z_2 unimodular complex number that satisfy z_1^2 + z_2^2 = 4 then (z_1 + bar(z_1))^2 ( z_2 + bar(z_2))^2 is equal to

Suppose arg (z) = - 5 pi//13 , then arg((z + bar(z))/(1+z bar(z))) is

arg((z)/(bar(z)))=arg(z)-arg(bar(z))

Let z_(1), z_(2) be two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1) - z_(2)| , then (z_(1))/(bar(z)_(1)) + (z_(2))/(bar(z)_(2)) equals

arg((1)/(bar(z)))=arg((zbar(z))/(bar(z)))

For all z in C, prove that (i) (1)/(2)(z+bar(z))=Re(z), (ii) (1)/(2i)(z-bar(z))=Im(z), (iii) z bar(z)=|z|^(2), (iv) z+bar(z))"is real", (v) (z-bar(z))"is 0 or imaginary".