If (n\pi + \frac{\pi}{3}), then. | MATH - INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS | SolveeIt

If $n\pi + \frac{\pi}{3}$ , then.

$n\pi \pm \frac{\pi}{3}$

$n$

$(1 - \cos\theta + 2i\sin\theta)^{- 1}$

$\frac{1}{3 + 5\cos\theta}$ or $\frac{1}{3 - 5\cos\theta}$

Answer

$\frac{1}{3 + 5\cos\theta}$ or $\frac{1}{3 - 5\cos\theta}$

Explanation

Given that $y = 0$

⇒ $\sin\theta = 0$

⇒ $\theta = 0$

Equating real and imaginary parts, we get

$x = 1$ or $x^{2} + y^{2} = 1^{2} + 0 = 1$ and $\mu + i\lambda = \frac{(p + i)^{2}}{2p - i} = \frac{(p^{2} - 1 + 2pi)(2p + i)}{(2p - i)(2p + i)}$

On solving we get $= \frac{2p(p^{2} - 2) + i(5p^{2} - 1)}{4p^{2} + 1}$ .

Question: If \(n\pi + \frac{\pi}{3}\), then....