what effect did he use?

matt bellamy uses a digitech whammy. you could definitely approximate the sound with a boss ps-5, ps-3, or hr-2 (probably not a ps-2), but the boss effects have a slightly more sterile sound to them than a whammy.
 
ps-3 is a pitch shifter delay. ps-5 has the harmonizer

i phaser is more like a linear phase. phase modulator varies the phase signal so you have more like a wavy phase. feel free to correct me if im mistaken hehe

the effect in the clip is basically a pitch up effect with delay. so any pedal/s that can do that will suffice
 
no this is not a phase effect. i dont think you can get this on a phaser

this is a pitch shift (octave up 1 or 2 steps) then add delay
 
he probably used a whammy + delay

if you're investing in pedals, these two are good investments anyway. you'll find a need for these two very much
 
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