For the complex number z, which of the following is true? Options: A . &nbsp z + ¯ z is real and z ¯ z is imaginary B . &nbsp z + ¯ z is imaginary and z ¯ z is real C . &nbsp Both z + ¯ z and z ¯ z are real. D . &nbsp Both z + ¯ z and z ¯ z are imaginary numbers

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

Question -

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

Options:

A .

z + ¯ z

is real and

z ¯ z

is imaginary

B .

z + ¯ z

is imaginary and

z ¯ z

is real

C . Both

z + ¯ z

and

z ¯ z

are real.

D . Both

z + ¯ z

and

z ¯ z

are imaginary numbers

Answer: Option C
:
C

Let $z = x + i y$
Here, $z + ¯ z = (x + i y) + (x - i y) = 2 x$ (Real)

And $z ¯ z = (x + i y) (x - i y) = x^{2} + y^{2}$ (Real).

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