Division of Complex Numbers in Polar Form/Examples/(3 cis pi by 6) (2 cis -5 pi by 4) (6 cis 5 pi by 3) (4 cis 2 pi by 3)^-2/Mistake
< Division of Complex Numbers in Polar Form | Examples | (3 cis pi by 6) (2 cis -5 pi by 4) (6 cis 5 pi by 3) (4 cis 2 pi by 3)^-2
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Source Work
1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.)
- Chapter $1$: Complex Numbers
- Supplementary Problems: De Moivre's Theorem: $89 \ \text {(d)}$
Mistake
- Evaluate each of the following:
- ... $\dfrac {\paren {3 e^{\pi i / 6} } \paren {2 e^{- 5 \pi i / 4} } \paren {6 e^{5 \pi i / 3} } } {\paren {4 e^{2 \pi i / 3} }^2}$
- Ans. $3 \sqrt 2 / 2 - \paren {3 \sqrt 3 / 2} i$
Correction
The correct solution is:
- $-\dfrac {9 \sqrt 2} 8 - \dfrac {9 \sqrt 2} 8 i$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: De Moivre's Theorem: $89 \ \text{(d)}$