Rationalizing complex number

Question

I have this equation from electronic task: \$I_{1} = \frac{u}{1200-j4416}\$.

How to remove the complex from the denominator?

I'm getting this, is this right? -48(92j-25)

Answer 1

You have\begin{align}\frac u{1200-4416j}&=\frac{u(1200+4416j)}{1\,200^2+4\,416^2}\\&=\left(\frac{25}{436\,272}+\frac{23}{109\,068}j\right)u\\&=\frac{25+92j}{436\,272}u.\end{align}

Answer 2

Well, assuming that $i^2=\text{j}^2=-1$ and $\text{u}\in\mathbb{C}$, we get:

$$\frac{\Re\left(\text{u}\right)+\Im\left(\text{u}\right)i}{1200-4416i}=\frac{\Re\left(\text{u}\right)+\Im\left(\text{u}\right)i}{1200-4416i}\cdot\frac{1200+4416i}{1200+4416i}=$$ $$\frac{\left(\Re\left(\text{u}\right)+\Im\left(\text{u}\right)i\right)\left(1200+4416i\right)}{1200^2+4416^2}\tag1$$