If `z=2-3i` show that `z^2-4z+13=0` and hence find the value of `4z^3-3z^2+169.`

If z=1+2i , show that z^(2)-2z+5=0 . Hence find the value of z^(3) +7z^(2)-z+16 .

If z=4+isqrt(7) , then find the value of z^2-4z^2-9z+91.

If z=2−3i then z ^2−4z+13=

Show that if iz^3+z^2-z+i=0 , then |z|=1

Show that if iz^3+z^2-z+i=0 , then |z|=1

If x = 2, y = 3 and z = -1, find the values of : (2x-3y+4z)/(3x-z)

If complex number z(z!=2) satisfies the equation z^2=4z+|z|^2+(16)/(|z|^3) ,then the value of |z|^4 is______.

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 , find the minimum value of |z_1-z_2|