Just remember , when the power of the complex is more than 4, divide by 4 and consider the remainder.
Now , we know
i^0=1
i^1=i
i^2= -1
i^3= -i
Know, take 7
7%4=3(I’m trying to say that the remainder is 3. The expression I used is used in computer science don’t use it in maths xD )
So (a+ib)^7=(a+ib)^3
Expand this using (x+y)^3=x^3+y^3+ 3xy^2+3yx^2
Solving this, you get, (a+ib)^7= a^3-ib^3+ 3iba^2+3ab^2
