Let $S$ be the set of points in the complex plane corresponding to the unit circle.$(\;i.e.,\;S = \left\{ {Z:\left| Z \right| = 1} \right\})$.Consider the function.$f\left( z \right) = z{z^*},\;$ where$\;{z^*}$ denotes the complex conjugate of $z$. The $f\left( z \right)$ maps $S$ to which one the following in the complex plane?

Question

Let $S$ be the set of points in the complex plane corresponding to the unit circle.$(\;i.e.,\;S = \left\{ {Z:\left| Z \right| = 1} \right\})$.Consider the function.$f\left( z \right) = z{z^*},\;$ where$\;{z^*}$ denotes the complex conjugate of $z$. The $f\left( z \right)$ maps $S$ to which one the following in the complex plane?

TuteeHUB · Accepted Answer

the entire horizontal axis.

TuteeHUB · Answer

Unit circle.

TuteeHUB · Answer

horizontal axis line segment from origin to $\left( {1,\;0} \right)$

TuteeHUB · Answer

the point $\left( {1,\;0} \right)$

1.	Let \(S\) be the set of points in the complex plane corresponding to the unit circle.\((\;i.e.,\;S = \left\{ {Z:\left\| Z \right\| = 1} \right\})\).Consider the function.\(f\left( z \right) = z{z^},\;\) where\(\;{z^}\) denotes the complex conjugate of \(z\). The \(f\left( z \right)\) maps \(S\) to which one the following in the complex plane?
A.	Unit circle.
B.	horizontal axis line segment from origin to \(\left( {1,\;0} \right)\)
C.	the point \(\left( {1,\;0} \right)\)
D.	the entire horizontal axis.
Answer» D. the entire horizontal axis.

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