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

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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