If z = x +iy is a complex number with x,y ∈ Q and ∣z∣=1, then show that ∣∣z2n−1∣∣ is a rational number for every n ∈ N.

Click here to view the solution.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

If z = x +iy is a complex number with x,y Q and {|{z}|}={1},

Question

If z = x +iy is a complex number with x,y $\in$ Q and $∣ z ∣ = 1$ , then show that $∣ ∣ z^{2 n} - 1 ∣ ∣$ is a rational number for every n $\in$ N.

Views: 653 students

Found 5 tutors discussing this question

Jack Discussed

If z = x +iy is a complex number with x,y

\in

Q and

∣ z ∣ = 1

, then show that

∣ ∣ z^{2 n} - 1 ∣ ∣

is a rational number for every n

\in

13 mins ago

Discuss this question LIVE

13 mins ago

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text

If z = x +iy is a complex number with x,y

\in

Q and

∣ z ∣ = 1

, then show that

∣ ∣ z^{2 n} - 1 ∣ ∣

is a rational number for every n

\in