z-1 is a factor of g(z)=2z-2 true or false
Answers
Answer:
hope it's helpful ...
Step-by-step explanation:
Correct option is A)
Step-by-step explanation:
if z unimodular then |z|=1 also use property of moduls i.e z
z
ˉ
=∣z∣
2
given z
2
is not unimodular ∣z∣
2
=1
and
2−z
1
z
ˉ
2
z
1
−2z
2
is unimodular
2−z
1
z
ˉ
2
z
1
−2z
2
=1
⇒∣z
1
−2z
2
∣
2
=∣2−z
1
z
ˉ
2
∣
2
⇒(z
1
−2z
2
)(
z
ˉ
1
−2
z
ˉ
2
)=(2−z
1
z
ˉ
2
)(2−
z
ˉ
1
z
2
)
∵z
z
ˉ
=∣z∣
2
⇒∣z
2
∣
2
+4∣z
2
∣
2
−2
z
ˉ
1
z
2
−2z
1
z
ˉ
2
=0
⇒(∣z
2
∣
2
−1)(∣z
1
∣
2
−4)=0
∣z
2
∣
=1
z
1
=x+iy
x
2
+y
2
=(2)
2
z
1
lies on radius is 2.
Hence ∣z
1
∣=2.