If z is a complex number, show that the sum of z and its conjugate...

Isa Trevino

Isa Trevino

Answered

2021-01-31

If z is a complex number, show that the sum of z and its conjugate is a real number.

Answer & Explanation

SoosteethicU

SoosteethicU

Expert

2021-02-01Added 102 answers

Given z is a complex number.
Let z=x+iy
We know that conjugate of a complex number is given by changing sign of imaginary part.
Conjugate of given complex number z will be:
z=x−iy
Now, sum of complex number z and its conjugate will be:
z+z=(x+iy)+(xiy)=x+iy+xiy=2x
Therefore, sum of z and it conjugate is real number.

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