Complex Numbers
Given the complex number:
z = 2 + 5i
The conjugate of z is another complex number with the same real part and its imaginary part as the inverse of z, that is:
[tex]\bar{z}=2-5i[/tex]
The product of z and its conjugate is:
[tex]z\cdot\bar{z}=(2+5i)(2-5i)[/tex]
Operating:
[tex]\begin{gathered} z\cdot\bar{z}=2^2+5^2 \\ z\cdot\bar{z}=4+25 \\ z\cdot\bar{z}=29 \end{gathered}[/tex]
This is the square of the distance of the point z to the origin, thus:
[tex]|z|=\sqrt[]{29}[/tex]
