Solve that equation `z^2+|z|=0` , where `z` is a complex number.

If z is a complex number then

Solve the equation z^(2)=bar(z) where z=x+iy

Let z_(1) and z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number, assume that the origin z_(1) and z_(2) form an equilateral triangle , then

The number of solutions of equation z^(2) + barz = 0 , where z in C are

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Solve the following equations. 6=z+2

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

Solve the following equations. z/(z+15)=4/9

If z_(1),z_(2)and z_(3) are the vertices of an equilateral triangle with z_0 as its circumcentre , then changing origin to z_0 ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.

A complex number z is said to be the unimodular if |z|=1 . Suppose z_(1) and z_(2) are complex numbers such that (z_(1)-2z_(2))/(2-z_(1)barz_(2)) is unimodular and z_(2) is not unimodular. Then the point z_(1) lies on a