Question

True or false: the product of a complex number and it’s conjugate is a real number

Answer 1

$a,b\in\mathbb{R}\\ z=a+bi\\ \overline{z}=a-bi\\\\ z\cdot\overline{z}=(a+bi)(a-bi)=a^2+b^2$

If $a,b\in\mathbb{R}$ then also $(a^2+b^2)\in\mathbb{R}$, so it's true.

Answer 2

HI THERE !!

yes, this is true, the product of a complex number and its conjugate is its real number!!


have a good day :)