Prove that the circles `z bar z +z( bar a )_1+bar z( a )_1+b_1=0 ,b_1 in R and z bar z +z( bar a )_2+ bar z a_2+b_2k=0,b+2 in R` will intersect orthogonally if `2R e(a_1( bar a )_2)=b_1+b_2dot`

Prove that the circles z bar z +z( bar a )_1+bar z( a )_1+b_1=0 ,b_1 in R and z bar z +z( bar a )_2+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1( bar a )_2)=b_1+b_2dot

Prove that the circles z bar z +z( bar a _1)+bar z( a_1 )+b_1=0 ,b_1 in R and z bar z +z( bar a _2)+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1 bar a _2)=b_1+b_2dot

Prove that the circles z bar z +z( bar a _1)+bar z( a_1 )+b_1=0 ,b_1 in R and z bar z +z( bar a _2)+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1 bar a _2)=b_1+b_2dot

Prove that the circles zbar(z)+z(bar(a))_(1)+bar(z)(a)_(1)+b_(1)=0,b_(1)in R and zbar(z)+z(bar(a))_(2)+bar(z)a_(2)+b_(2)k=0,b+2in R will intersect orthogonally if 2Re(a_(1)(bar(a))_(2))=b_(1)+b_(2)

Prove that the circle zbar(z)+zbar(a)_(1)+bar(z)a_(1)+b_(1)=0;b_(1)varepsilon R and zbar(z)+zbar(a)_(2)+bar(z)a_(2)+b_(2)=0;b_(2)varepsilon R will intersect orthogonally if 2Re(a_(1)bar(a)_(2))=b_(1)+b_(2)

Identify the locus of z if bar z = bar a +(r^2)/(z-a).

Identify the locus of z if bar z = bar a +(r^2)/(z-a).

Identify the locus of z if bar z = bar a +(r^2)/(z-a).

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