$ ext{Find the Real Part of a Complex Number on the Unit Circle}$
Answer 1
Ava Martin
Consider a complex number $z$ on the unit circle in the complex plane. The unit circle can be represented as $|z| = 1$. If $z = e^{i\theta}$, find the real part of $z$.
Solution:
Since $z = e^{i\theta}$, we can use Euler’s formula, which states:
$e^{i\theta} = \cos \theta + i \sin \theta$
The real part of $z$ is therefore:
$ \cos \theta $
Answer 2
Emma Johnson
Given that a complex number $z$ is on the unit circle, such that $|z| = 1$ and $z = e^{i heta}$, we need to determine the real part of $z$.
Solution:
Using Euler’s formula:
$ z = e^{i heta} = cos heta + i sin heta $
The real part of $z$ is:
$cos heta$
Answer 3
Matthew Carter
If a complex number $z$ lies on the unit circle, $|z| = 1$, and $z = e^{i heta}$, then find the real part of $z$.
Solution:
Using Euler’s formula:
$ z = e^{i heta} = cos heta + i sin heta $
The real part of $z$ is:
$cos heta$
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