Question

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

Answer 1

The correct answer is:

D.

I just took the quiz and got it right.

Answer 2

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