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Question

Let S be the set of points in the complex plane corresponding to the unit circle. That is S=[z:|z|=1]. Consider the function f(z)=zzāˆ— wherer zāˆ— denotes wth complex conjugate of z. The f(z) maps S to which one of the following in the complex plane

A
unit circle
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B
horizontal axis line segment from orgin to (1,0)
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C
the point (1,0)
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D
the entire horizontal axis
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Solution

The correct option is C the point (1,0)
f(z)=zz where Z=¯¯¯¯Z
s=z:|z|=1
f(z)=z¯¯¯z=|z2|=1=1+0i=(1,0)
f(z) maps s to the (1,0) in the complex plane.

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