Home
Class 12
MATHS
If a point z1 is a reflection of a point...

If a point `z_1` is a reflection of a point `z_2` through the line `b bar z + bar b z + c = 0, b!=0` in the argand plane. Then `b bar(z_1) + bar b z_2`

Text Solution

Verified by Experts

`|z-z_1|=|z-z_2|`
`|z-z_1|^2=|z-z_2|^2`
`(z-z_1)(overlinez-overlineZ_1)=((z-z_2)(overlinez-overlineZ_2)`
`overlineZ(-Z_1+Z_2)+Z(-overlineZ_1+overlineZ_2)+Z_1overlineZ_1-Z_2overlineZ_2=0-(1)`
`boverlineZ+overlinebZ+C=0`
`b/(Z_2-Z_1)=overline b/(overlineZ_2-overlineZ_1)=C/(Z_1overlineZ_1-Z_2overlineZ_2)=K`
`boverlineZ_1+overlinebZ_2`
`overlineZ(Z_2-Z_1)K+K(overlineZ_2-overlineZ_1)Z_2`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If a point z_(1) is the reflection of a point z_(2) through the line b barz+barbz=c, b in 0 , in the Argand plane, then b barz_(2)+ barb z_(1)=

If a point z_(1) is the reflection of a point z_(2) through the line b barz+barbz=c, b in 0 , in the Argand plane, then b barz_(2)+ barb z_(1)=

Let bar b z+b bar z=c, b ne 0 , be a line in the complex plane, where bar b is the complex conjugate of b. If a point z_1 is the reflection of a point z_2 through the line, then show that : c= bar z_1 b+z_2 bar b .

Let barbz+b(barz)=c,b!=0 be a line the complex plane, where bar b is the complex conjugate of b. If a point z_1 i the reflection of the point z_2 through the line then show that c=barz_1b+z_2barb

Let barbz+b(barz)=c,b!=0 be a line the complex plane, where bar b is the complex conjugate of b. If a point z_1 i the reflection of the point z_2 through the line then show that c=barz_1b+z_2barb

Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the complex conjugaste of b. If a point z_1 i the reflection of the point z_2 through the line then show that c=barz_1b+z_2barb

The equation z bar z+a bar z+bar a z+b=0, b in R represents a circle if :