1.if z1 and z2 are two complex numbers then z=nz1+mz2/m+n is a complex number which divides the line joining  points z1 and z2 in the ratio m:n.

 

2.if the points z1,z2,z3,z4 are on the argand plane,then the line joining z4 and z3 is inclined to the line joining z2 and z1 at the angle theta=arg(z1-z2/z3-z4)

 

3.the equation of line joining z1 and z2 is given by z=t z1+ (1-t) z2 where t is a real parameter..

 

4.the equation mod z-z1/z-z2=k will represent a circle if k is not equal to 1 and a line if k is equal to 1.

 

5.if mod z-z1 + mod z-z2=2a where 2a>mod z1-z2,then the point z describes an ellipse having foci at z1 and z2

 

6.if mod z-z1 - mod z-z2=2a where 2a<mod z1-z2,then the point z describes a hyperbola having foci at z1 and z2

 

7.the triangle whose vertices are z1,z2,z3 is equilateral if

     1.1/z1-z2 +1/z2-z3 + 1/z3-z1=0

      2. z1^2+z2^2+z3^2=z1z2+z2z3+z3z1..

8.if the complex numbers z1,z2,z3 are in A.P.,then they lie on a line..

 

9.a point z1 is said to be interior or exterior of circle mod z-z nought=r if mod z1-z nought < r or mod z1-z nought >r..

 

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