First slide

Introduction to sets

Question

If $n ∣ q and A = \{z \in C : z^{n} = 1\}$ $B = \{z : z^{q} = 1\}$ then

Moderate

A

$A = B$
B

$A \cap B = {1}$
C

$B \subseteq A$
D

$A \subset B$

Solution

$q = p n$ for some $p \in N$
$z^{q} - 1 = {(z^{n})}^{p} - 1 = (z^{n} - 1) (z^{(p - 1) n} + \dots + z^{n} + 1)$
Every root of $z^{n} - 1$ is a root of $z^{q} - 1$ and every root of $z^{(p - 1) n} + \dots + z^{n} + 1 = 0$ is also a root of $z^{q} - 1$ Hence. $A \subset B ∣$
and $A \cap B = A$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App