Question

Find the quotient of the complex numbers. Express your answer in trigonometric form.
z1 = 12(cos(320 degrees) + isin(320 degrees))
z2 = 4(cos(80 degrees) + isin(80 degrees))

Answer 1

\[z_{1}=12\left[ \cos \left( 320 \right) ^\circ+isin \left( 320 \right)^\circ\right]=12e ^{320i}\]
\[z_{2}=4\left[ \cos \left( 80 \right) ^\circ+isin \left( 80 \right)^\circ\right]=4e ^{80i}\]
\[\frac{ z_{1} }{z_{2} }=\frac{ 12 e ^{320^\circ i} }{ 4e ^{80^\circ i} }=3e ^{(320-80) ^\circ i}\]
\[\frac{ z_{1} }{ z_{2} }=3e ^{240^\circ i}\]
\[\frac{ z_{1} }{ z_{2} }=3\left[ \cos(240)^\circ+i \sin(240)^\circ \right]\]