Let `|(( z )_1-2( z )_2)//(2-z_1( z )_2)|=1a n d|z_2|!=1,w h e r ez_1a n dz_2` are complex numbers. Show that `|z_1|=2.`

Let |(( bar z _1)-2( bar z _2))//(2-z_1( bar z _2))|=1 and |z_2|!=1 ,where z_1 and z_2 are complex numbers. Show that |z_1|=2.

Let |(z_(1) - 2z_(2))//(2-z_(1)z_(2))|= 1 and |z_(2)| ne 1 , where z_(1) and z_(2) are complex numbers. shown that |z_(1)| = 2

If |(z-z_1)/(z-z_2)|=3,w h e r ez_1a n dz_2 are fixed complex numbers and z is a variable complex number, then z lies on a (a).circle with z_1 as its interior point (b).circle with z_2 as its interior point (c).circle with z_1 as its exterior point (d).circle with z_2 as its exterior point

If a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n z_1+z_2=0 b. z_1z_2=1 c. z_1=z _2 d. none of these

Let z_1=r_1(costheta_1+isintheta_1)a n dz_2=r_2(costheta_2+isintheta_2) be two complex numbers. Then prove that |z_1+z_2|^2=r1 2+r2 2+2r_1r_2cos(theta_1-theta_2) or |z_1+z_2|^2=|z_1|^2+|z_2|^2+2|z_1||z_2|^()_cos(theta_1-theta_2)

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

If z_1, z_2a n dz_3, z_4 are two pairs of conjugate complex numbers, find the a rg((z1)/(z4))+a rg((z2)/(z3)) =0

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

For any two complex number z_1a n d\ z_2 prove that: |z_1+z_2|geq|z_1|-|z_2|