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?

 

Thanks         

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?