Q. If $iz^{4} + 1 = 0$, then $z$ can be take the value
A) $\frac{1 + i}{\sqrt{2}}$
B) $\cos{\frac{\pi}{8} + i\sin\frac{\pi}{8}}$
C) $\frac{1}{4i}$
D) $i$
Explanation
(b)
Given, $iz^{4} + 1 = 0$
$\Rightarrow \ \ \ z^{4} = i$
$\Rightarrow \ \ z = \left( \cos{\frac{\pi}{2} + i\sin\frac{\pi}{2}} \right)^{1/4}$
By using De-Moivre’s theorem, we get
$z = \cos{\frac{\pi}{8} + i\sin\frac{\pi}{8}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.