Prove (z1/z2) the whole bar = z1 bar /z2 bar ( bar means conjugate) - Maths - Complex Numbers and Quadratic Equations

Question

Prove (z1/z2) the whole bar = z1 bar /z2 bar ( bar means conjugate)

Neha Sethi · Accepted Answer

Dear student

To show: z1z2=z1z2  ,z2≠0We have, z1z2=a1+ib1a2+ib2=a1a2+b1b2a22+b22+ia2b1-a1b2a22+b22So, z1z2=a1a2+b1b2a22+b22-ia2b1-a1b2a22+b22    
1Now, z1z2=z1×1z2=a1-ib1a2a22+b22+ib2a22+b22=a1a2+b1b2a22+b22-ia2b1-a1b2a22+b22   
2From 1 and 2 we getz1z2=z1z2  ,z2≠0
Regards

Prove (z1/z2) the whole bar = z1 bar /z2 bar. ( bar means conjugate).