Question

Find the quotient z^1/z^2 of the complex numbers. Leave answer in polar form.

Answer 1

\[\let z =r e ^{\iota \theta} \]
\[\frac{ z1 }{ z2 }=\frac{ r1 e ^{\iota \theta1} }{ r2e ^{\iota \theta2}}=\frac{ r1 }{r2 }e^{\iota \left( \theta1-\theta2 \right)}\]\]
\[=\frac{ r1 }{ r2}\left\{ \cos \left( \theta1-\theta2 \right)+\iota \sin \left( \theta1-\theta2 \right) \right\}\]
plugging the values of r1,r2,\[\theta 1,\theta 2\]
we get the required solution

Answer 2

Working this out...........

Answer 3

sin(θ1-θ2)+cos(θ1-θ2)/r

Answer 4

r1=1/8
r2=1/3
r1/r2=1/8*3/1=3/8
\[\theta 1=\frac{ 2\pi }{3 },\theta2=\frac{ \pi }{ 4 },\]
\[\theta1-\theta2=\frac{ 8\pi-3\pi }{12 }=\frac{ 5\pi }{12 }\]
\[\frac{ z1 }{ z2 }=\frac{ 3 }{ 8 }e ^{\iota \frac{ 5\pi }{ 12 }}=\frac{ 3 }{ 8 }\left( \cos \frac{ 5\pi }{ 12}+\iota \sin \frac{ 5\pi }{12 } \right)\]

Answer 5

Thank you very much

Answer 6

yw