Express the seventh root of unity in standard form a+bi

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

The correct answer is:

D.

I just took the quiz and got it right.