HDMI Splitter questions?

So basically I have a computer which I use for gaming and media like netflix. I use a normal monitor for gaming and a tv for media. I wanted to buy a HDMI splitter like this one, but I realised I don't need a splitter with multiple inputs and one output. I need the opposite as I only have one input my computer and two outputs. So do I need something like this. But why do all the Hdmi splitters that come up when I type in 'HDMI splitter 1 input 2 output' need external power and have to be like a brick rather than like the first one. I don't need both of the displays to run at the same time just to be switchable like the first product. Is there a name for what I'm looking for?



Get the first one and plug the output into your computer and both the monitor and the t.v into the splitter.. would that work?