First slide
Algebra of complex numbers

Let z1 and z2, be two distinct complex numbers and let z=(1t)z1+t z2 for some real number t with 0 <  t < 1. if arg (w) denotes the principal argument of a non-zero complex number , then


Given z=(1t)z1+tz2(1t)+t

Clearly, z divides z, and z, in the ratio of t :(1 - t), 0<t<1

AP+BP=AB i.e., zz1+zz2=z1z2.

and argzz1=argz2z=argz2z1

Also ,argzz1=argz2z1


zz1z2z1 is purely real.

zz1z2z1=z¯z¯1z¯2z¯1 or zz1z¯z¯1z2z1z¯2z¯1=0

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