Q(zq)  is the foot of perpendicular drawn from P(zp)  to the line az¯+za¯+b=0, b∈R and 'a' is complex number, then:

Since a is perpendicular vector to the line.zq−zp=λa,  λ∈Ra¯(zp+λa)+a(z¯p+λa¯)+b=0⇒      az¯p+a¯zp+b+2λaa¯=0Also 2a¯zq−2a¯zp=2λaa¯∴        az¯p+a¯zp+b+2a¯zq−2a¯zp=0⇒    2a¯zq+az¯p−a¯zp+b=0