Find the complex number z such that it satisfies the equation, `2barz+3+5i=iz`

Find the complex number z if z^2+barz =0

The complex number z satisfying the equation |z-i|=|z+1|=1

Find a complex number z satisfying the equation z+sqrt(2)|z+1|+i=0

Fid the number of complex numbers which satisfies both the equations |z-1-i|=sqrt(2) and |z+1+i|=2

Find the complex number z satisfying the equations |(z-12)/(z-8i)|=(5)/(3),|(z-4)/(z-8)|=1

Find the complex number omega satisfying the equation z^(3)=8i and lying in the second quadrant on the complex plane.

Find the locus of a complex number z=x+ iy satisfying the relation |2z+3i|<=|2z+5|. Illustrate the locus in Argand plane.