Question

$(\sqrt{3}+i)^{10} + (\sqrt{3}-i)^{10} =$

• A. $1024\sqrt{3}$
• B. 1024
• C. 2048
• D. $512\sqrt{3}$

Hint:

For expressions of the form $(x+iy)^n + (x-iy)^n$, using De Moivre's theorem is the most efficient method. Remember that the sum will be $2r^n\cos(n\theta)$ and the difference will be $2ir^n\sin(n\theta)$.

Answer 1

The Correct Option is B