Consider the following two statements : Statement I : For any two non-zero complex numbers z₁, z₂ , ( |z₁ |+ |z₂ | ) | z₁ |z₁ | + z₂ |z₂ | | 2 ( |z₁ |+ |z₂ | ) , and Statement II : If x, y, z are three distinct complex numbers and a , b , c are three positive real numbers such that a |y-z| = b |z-x| = c |x-y| , then a ^2 y-z + b ^2 z-x + c ^2 x-y =1 . Between the above two statements,

Step-by-step solution

Statement I : ( |z₁ |+ |z₂ | ) | z₁ |z₁ | + z₂ |z₂ | | Since | z₁ |z₁ | + z₂ |z₂ | | | z₁ |z₁ | |+ | z₂ |z₂ | | aligned & | z₁ |z₁ | + z₂ |z₂ | | |z₁ | |z₁ | + |z₂ | |z₂ | & | z₁ |z₁ | + z₂ |z₂ | | 2 aligned ( |z₁ |+ |z₂ | ) ( | z₁ |z₁ | + z₂ |z₂ | | ) 2 ( |z₁ |+ |z₂ | ) statement I is correct For Statement II : aligned & a |y-z| = b |z-x| = c |x-y| & a^2 |y-z|^2 = b^2 |z-x|^2 = c^2 |x-y|^2 = & a^2= (|y-z|^2 )= (y-z)( y - z ) & b^2= (z-x)( z - x ) and c^2= (x-y)( x - y ) & a^2 y-z + b^2 z-x + c^2 x-y = ( y - z + z