Question

Z1 and z2 are two complex numbers such that z1-2z2/2-z1z2 is unimodular

Answer 1

Answer:

Step-by-step explanation:

if z unimodular then |z|=1 also use property of moduls i.e zz`=|z|^2

given z^2 is not unimodula |z|2≠1

and  z1-2z2/2-z1z2 is unimodular

z1-2z2/2-z1z2 =1

⇒ |z1-2z2|^2=|2-z1z2`|^2

⇒(Z1-2Z2)(Z1`-2Z2` )=(2-Z1Z2` )(2-Z1`Z2)

∵ZZ`=|z|^

⇒|Z2|^2+4|Z2|^2-2Z1`Z2-2Z1Z2`                            

⇒(|Z1|^2-1)(|Z1|-4)=0

|Z2|≠1

|zZ|=2

Z1=X+iy

X^2+Y^2=(2)^2

z1 lies on redius is 2

hope it is helpful