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?