Question

The general value of the real angle $\theta$, which satisfies the equation, (cos$\theta$ + i sin$\theta$) (cos2$\theta$ + i sin2$\theta$)........ (cosn$\theta$ + i sinn$\theta$) = 1 is given by, (assuming k is an integer)

• A. $\frac{2k\pi}{n+2}$
• B. $\frac{4k\pi}{n\left(n+1\right)}$
• C. $\frac{4k\pi}{n+1}$
• D. $\frac{6k\pi}{n\left(n+1\right)}$

Answer 1

Answer: (B)

$e^{i\theta}\cdot e^{i\left(2\theta\right)}\cdot e^{i\left(3\theta\right)}\ldots e^{i\left(n\theta\right)} = 1\,\Rightarrow \,e^{i\left(\theta \frac{\left(n\left(n+1\right)\right)}{2}\right)} = e^{i2k\,\pi\,\Rightarrow \,\theta = \frac{4k\pi}{n\left(n+1\right)}}$