Let z satisfy |z|=1 and z=1- z . Statement 1: z is a real number. Statement 2 : Principal argument of z is 3

Step-by-step solution

Let z=x+i y, z =x-i y aligned & Now, z=1- z & x+i y=1-(x-i y) & 2 x=1 x= 1 2 & Now, |z|=1 x^2+y^2=1 y^2=1-x^2 & y= 3 2 aligned Now, = y x ( is the argument ) = 3 2 1 2 (+ve since only principal argument) gathered = 3 = ⁻¹ 3 = 3 gathered Hence, z is not a real number So, statement-1 is false and 2 is true.