GATE EE 2014 Set 1 — Question 15
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Engineering Mathematics → Complex Variables
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Question
Let be the set of points in the complex plane corresponding to the unit circle. (That is, ). Consider the function where denotes the complex conjugate of . The maps to which one of the following in the complex plane
Correct answer
(C) the point (1, 0)
Solution
The set is the unit circle in the complex plane, defined by .
The function is given as .
Using the property of complex numbers where , we can write:
For all , , therefore:
.
In the complex plane, the value corresponds to the point .
Hence, the correct option is (C).
The function is given as .
Using the property of complex numbers where , we can write:
For all , , therefore:
.
In the complex plane, the value corresponds to the point .
Hence, the correct option is (C).
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