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Question

For the complex number z, which of the following is true?



A

z+¯z is real and z¯z is imaginary

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B

z+¯z is imaginary and  z¯z is real

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C

Both z+¯z and z¯z are real.

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D

Both z+¯z and z¯z are imaginary numbers

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Solution

The correct option is C

Both z+¯z and z¯z are real.


Let z=x+iy

Here,  z+¯z=(x+iy)+(xiy)=2x (Real)

And z¯z=(x+iy)(xiy)=x2+y2 (Real).


Mathematics

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