Division of Complex Numbers in Polar Form/Examples

Examples of Use of Division of Complex Numbers in Polar Form

Example: $\dfrac {\paren {2 \cis 15 \degrees}^7} {\paren {4 \cis 45 \degrees}^3}$

$\dfrac {\paren {2 \cis 15 \degrees}^7} {\paren {4 \cis 45 \degrees}^3} = \sqrt 3 - i$

Example: $\dfrac {\paren {8 \cis 40 \degrees}^3} {\paren {2 \cis 60 \degrees}^4}$

$\dfrac {\paren {8 \cis 40 \degrees}^3} {\paren {2 \cis 60 \degrees}^4} = -16 - 16 \sqrt 3 i$

Example: $\dfrac {\paren {3 \cis \dfrac \pi 6} \paren {2 \cis \dfrac {-5 \pi} 4} \paren {6 \cis \dfrac {5 \pi} 3} } {\paren {4 \cis \dfrac {2 \pi} 3}^2}$

$\dfrac {\paren {3 \cis \dfrac \pi 6} \paren {2 \cis \dfrac {-5 \pi} 4} \paren {6 \cis \dfrac {5 \pi} 3} } {\paren {4 \cis \dfrac {2 \pi} 3}^2} = -\dfrac {9 \sqrt 2} 8 - \dfrac {9 \sqrt 2} 8 i$