Roots of Complex Number/Examples/Cube Roots of -11-2i/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: $99$
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 the cube roots of $-11 - 2 i$.
- Ans. ... $1 + 2 i, \dfrac 1 2 - \sqrt 3 + \paren {1 + \dfrac {\sqrt 3} 2} i, -\dfrac 1 2 - \sqrt 3 + \paren {\dfrac {\sqrt 3} 2 - 1} i$
Correction
The correct solution is:
- $\set {1 + 2 i, -\dfrac 1 2 + \sqrt 3 + \paren {-1 - \dfrac {\sqrt 3} 2} i, -\dfrac 1 2 - \sqrt 3 + \paren {-1 + \dfrac {\sqrt 3} 2} i}$
as demonstrated in Cube Roots of $-11 - 2 i$.
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Roots of Complex Numbers: $99$