Roots of Complex Number/Examples/5th Roots of -16 + 16 root 3 i/Mistake
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Source Work
1964: Murray R. Spiegel: Theory and Problems of Complex Variables
- Chapter $1$: Complex Numbers
- Supplementary Problems: Roots of Complex Numbers: $96 \ \text{(c)}$
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.
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Roots of Complex Numbers: $96 \ \text{(c)}$