Roots of Complex Number/Examples/5th Roots of -16 + 16 root 3 i/Mistake

Source Work

 * Chapter $1$: Complex Numbers
 * Supplementary Problems: $96 \ \text{(c)}$

This mistake can be seen in the 1981 printing of the second edition (1974) as published by Schaum: ISBN 0-070-84382-1

Mistake

 * Find all the indicated roots and locate them in the complex plane.
 * ... $\text {(c)}$ fifth roots of $-16 + 16 \sqrt 3 i$, ...


 * Ans. ... $\text {(c)}$ $2 \cis 48 \degrees$, $2 \cis 120 \degrees$, $2 \cis 192 \degrees$, $2 \cis 264 \degrees$, $2 \cis 336 \degrees$ ...

Correction
The correct solution is:
 * $2 \cis 24 \degrees$, $2 \cis 96 \degrees$, $2 \cis 168 \degrees$, $2 \cis 240 \degrees$, $2 \cis 312 \degrees$

as demonstrated in $5$th Roots of $-16 + 16 \sqrt 3 i$.

The mistake probably arose from mistaking $\dfrac {2 \pi} 3 = 240 \degrees$ when calculating the arguments in degrees.