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Let S be the set of points in the complex plane corresponding to the unit circle. (That i s, S = {z: | z| = 1}. Consider the function f(z) = zz* where z* denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane
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- Unit circle
- Horizontal axis line segment from origin to (1, 0)
- The point (1, 0)
- The entire horizontal axis
Correct Option: C
ƒ(Z) = Z.Z*
where Z* is conjugate of Z
∴ ƒ(Z) = | Z|²
= 1 + i.0
∴ ƒ(Z) maps S to the point (1, 0) in the complex plane
