Question

The sum of the products of the non-conjugate roots of $i^{1/4}$ taken two at a time is

• A. 2
• B. 0
• C. -1
• D. -2

Answer 1

Answer: (B)

Let $z=i^{1/4}$
$\Rightarrow z^4=i=e^{i\pi /2}$
$i\left(\frac{\pi }{8}\right),e^{i\left(\frac{5\pi }{8}\right)},e^{i\left(\frac{9\pi }{8}\right)}$ and $e^{i\left(\frac{13\pi }{8}\right)}$
and its roots are and there is no pair of conjugate roots.
So, sum of products of the roots (which are non-conjugate) of equation $z^4-i=0$ is zero.