# abstract algebra – degree of field expansion with a trick or not?

given $$[Bbb Q(a):Bbb Q]$$ and $$b = i cdot a$$With $$i$$ I would like to know an imaginary number $$[Bbb Q(a,b):Bbb Q]$$, I can use $$[Bbb Q(a,b):Bbb Q]=[Bbb Q(a,b):Bbb Q(a)] cdot [Bbb Q(a):Bbb Q]$$

Can you complete the degrees or do I have to do that with the minimal polynomial etc?