Question

which is also the square of the distance of the point z from the origin. (Plot z as a point in the "complex" plane in ordeto see this.)If z = 2 + 5i then z =and |z| =

Answer 1

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:

`\bar{z}=2-5i`

The product of z and its conjugate is:

`z\cdot\bar{z}=(2+5i)(2-5i)`

Operating:

`\begin{gathered} z\cdot\bar{z}=2^2+5^2 \\ z\cdot\bar{z}=4+25 \\ z\cdot\bar{z}=29 \end{gathered}`

This is the square of the distance of the point z to the origin, thus:

`|z|=\sqrt[]{29}`