If `8iz^3+12z^2-18z+27i=0,` then (a). `|z|=3/2` (b). `|z|=2/3` (c). `|z|=1` (d). `|z|=3/4`

If z = (1)/((2 + 3i)^(2)) then |z| =

If |z+3|^(2)-|z-3|^(2)=8 then the locus of z is

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that (z_(1) + z_(2)) z_(3) = z_(1) z_(3) + z_(2) z_(3)

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

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that z_(1)(z_(2) + z_(3)) = z_(1) z_(2) + z_(1) z_(3)

If z_1=5+12 ia n d|z_2|=4,t h e n (a)maximum (|z_1+i z_2|)=17 (b)minimum (|z_1+(1+i)z_2|)=13+4sqrt(2) (c)minimum |(z_1)/(z_2+4/(z_2))|=(13)/4 (d)maximum |(z_1)/(z_2+4/(z_2))|=(13)/3

If z_(1) = 1 - 3i, z_(2) = -4i and z_(3) = 5, show that (z_(1) + z_(2)) + z_(3) = z_(1) + (z_(2) + z_(3))

If | z_(1) | = 1, |z_(2)| = 2, |z_(3)| = 3 and |9z_(1)z_(2) + 4z_(1) z_(3) + z_(2) z_(3) = 12|, then the value of |z_(1) + z_(2) + z_(3)| is

If z_1, z_2 in C ,z_1^ 2 in R ,z_1(z_1^ 2-3z_2 ^2)=2 a n d z_2(3z_1 ^2-z_2^ 2)=11 , then the value of z_1^ 2+z_2^ 2 is a. 10 b. 12 c. 5 d. 8

If z_(1),z_(2), and z_(3) are three complex numbers such that |z_(1)| = 1, " " |z_(2)| = 2, " " |z_(3)| = 3 and |z_(1) + z_(2) + z_(3) | = 1, show that |9z_(1)z_(2) + 4 z_(1)z_(3) + z_(2)z_(3)| = 6 .