Let `z_1=10+6i` and `z_2=4+6idot` If `z` is any complex number such that the argument of `((z-z_1))/((z-z_2))` is `pi/4,` then prove that `|z-7-9i|=3sqrt(2)` .

Let z_1=6+i and z_2=4-3i . If z is a complex number such thar arg ((z-z_1)/(z_2-z))= pi/2 then (A) |z-(5-i)=sqrt(5) (B) |z-(5+i)=sqrt(5) (C) |z-(5-i)|=5 (D) |z-(5+i)|=5

If z_1=i z_2 and z_1-z_3=i(z_3-z_2) ,then prove that |z_3|=sqrt(2)|z_1|.

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

If z_1=10+6i and z_2=4+2i be two complex numbers and z be a complex number such that a r g((z-z_1)/(z-z_2))=pi/4 , then locus of z is an arc of a circle whose (a) centre is 5+7i (b) centre is 7+5i (c) radius is sqrt(26) (d) radius is sqrt(13)

If z be any complex number (z!=0) then arg((z-i)/(z+i))=pi/2 represents the curve

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+ 1/z is

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

Let z_(1),z_(2) and z_(3) be three complex number such that |z_(1)-1|= |z_(2) - 1| = |z_(3) -1| and arg ((z_(3) - z_(1))/(z_(2) -z_(1))) = (pi)/(6) then prove that z_(2)^(3) + z_(3)^(3) + 1 = z_(2) + z_(3) + z_(2)z_(3) .