Question 1174537
<br>
{{{13i = 13*cis(pi/2)}}}<br>
By deMoivre's Theorem, the primary square root is<br>
{{{sqrt(13i) = sqrt(13)*cis((pi/2)/2) = sqrt(13)*cis(pi/4)}}}<br>
The n n-th roots of a complex number have the same magnitude, and they are separated in the complex plane by angles of (2pi)/n.<br>
For this problem with square roots, the other square root is (2pi)/2 = pi radians past the primary square root: {{{sqrt(13)*cis(5pi/4)}}}<br>
ANSWERS:
{{{sqrt(13)*cis(pi/4)}}}
{{{sqrt(13)*cis(5pi/4)}}}<br>