Find the cosine of a point on the unit circle in the complex plane
Answer 1
Joseph Robinson
Given a point on the unit circle in the complex plane, represented by the complex number $z = e^{i\theta}$, determine the value of $\cos(\theta)$.
Since $z = e^{i\theta}$, we know that:
$z = \cos(\theta) + i\sin(\theta)$
Thus, the real part of $z$ is $\cos(\theta)$. Therefore, the value of $\cos(\theta)$ is simply the real part of $z$.
Hence, if $z = e^{i\theta} = \cos(\theta) + i\sin(\theta)$, then $\cos(\theta) = \text{Re}(z)$.
Answer 2
Maria Rodriguez
Given the point $z$ on the unit circle in the complex plane, where $z = e^{i heta}$, we are asked to find $cos( heta)$.
We know Euler’s formula states:
$e^{i heta} = cos( heta) + isin( heta)$
Therefore, the real part of $z$ (which is $e^{i heta}$) is $cos( heta)$. So, the value of $cos( heta)$ is the real part of $z$.
Thus, if $z = e^{i heta}$, then $cos( heta) = ext{Re}(z)$.
Answer 3
Abigail Nelson
Given $z = e^{i heta}$ on the unit circle, find $cos( heta)$.
From Euler’s formula:
$e^{i heta} = cos( heta) + isin( heta)$
The real part of $z$ is $cos( heta)$.
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