1. If `z_1` and `z_2` are two complex numbers, then
(i) `|z_1 -z_2|` is the distance between the points affixes `z_1` and `z_2`.
(ii) `(mz_2 + nz_1)/( m +n)` is the affix of the point dividing the line joining the points with affixes `z_1` and `z_2` in the ratio `m : n` internally, where `m != n`.
(iii) `(mz_2 - nz_1 )/(m -n)` is the affix of the point dividing the line joining the points with affixes `z_1` and `z_2 `in the ratio `m : n ` externally, where `m != n`
(iv) If the affixes of the vertices of the triangle are `z_1, z_2` and `z_3` , then the affix of its centroid is `(z_1 + z_2 + z_3 ) /3`
2. Three points with affixes `z_1, z_2 , z_3` are collinear, if
`|( z_1 , barz_1 ,1 ), ( z_2 , barz_2, 1),(z_3, barz_3, 1) | = 0`
3. (i) `|z -z_1| = r` represents the circle with centre `z_1` and radius `r.`
(ii) `| z - z_1 | < r` represents the interior of the circle with centre `z_1` and radius ` r.`
4. `|(z -z_1 ) / (z -z_2) | = k ` represents a circle, if `k != 1` and if `k =1` , then it represent a straight line which is the perpendicular bisector of the line segment joining points with affixes `z_1` and `z_2`.
5. `(z-z_1) (bar z- barz_2) + (bar z - barz_1) (z - z_2) = 0` represents the circle with line joining points with affixes `z_1` and `z_2` as a diameter.
6. If `z_1, z_2` and `z_3` are the affixes of the points `A, B, C` respectively , then the angle between `AB` and `AC` is given by `arg((z_3 - z_1 )/( z_2 - z_1 ) )`
1. If `z_1` and `z_2` are two complex numbers, then
(i) `|z_1 -z_2|` is the distance between the points affixes `z_1` and `z_2`.
(ii) `(mz_2 + nz_1)/( m +n)` is the affix of the point dividing the line joining the points with affixes `z_1` and `z_2` in the ratio `m : n` internally, where `m != n`.
(iii) `(mz_2 - nz_1 )/(m -n)` is the affix of the point dividing the line joining the points with affixes `z_1` and `z_2 `in the ratio `m : n ` externally, where `m != n`
(iv) If the affixes of the vertices of the triangle are `z_1, z_2` and `z_3` , then the affix of its centroid is `(z_1 + z_2 + z_3 ) /3`
2. Three points with affixes `z_1, z_2 , z_3` are collinear, if
`|( z_1 , barz_1 ,1 ), ( z_2 , barz_2, 1),(z_3, barz_3, 1) | = 0`
3. (i) `|z -z_1| = r` represents the circle with centre `z_1` and radius `r.`
(ii) `| z - z_1 | < r` represents the interior of the circle with centre `z_1` and radius ` r.`
4. `|(z -z_1 ) / (z -z_2) | = k ` represents a circle, if `k != 1` and if `k =1` , then it represent a straight line which is the perpendicular bisector of the line segment joining points with affixes `z_1` and `z_2`.
5. `(z-z_1) (bar z- barz_2) + (bar z - barz_1) (z - z_2) = 0` represents the circle with line joining points with affixes `z_1` and `z_2` as a diameter.
6. If `z_1, z_2` and `z_3` are the affixes of the points `A, B, C` respectively , then the angle between `AB` and `AC` is given by `arg((z_3 - z_1 )/( z_2 - z_1 ) )`