Question

How to simplify |z*(z+1)|=|z+zi|^2
z* is complex conjugate and i is an imaginary unit

Answer 1

Let \(z=a+bi\).
\[\begin{align*}
|z^*(z+1)|&=|z+zi|^2\\\\
|(a-bi)(a+bi+1)|&=|a+bi+ai-b|^2\\\\
|a^2+b^2+a-bi|&=|a-b+(a+b)i|^2\\\\
\sqrt{(a^2+b^2+a)^2+b^2}&=\sqrt{(a-b)^2+(a+b)^2}
\end{align*}\]

Answer 2

Ahh I understand, but without the root on the right side since we have square root there to cancel it out.

Answer 3

Right! Sorry for the confusion.