Question

Given that z = 10 cis 30° and w = 5 cis 10°, find z/w. Leave your answer in polar form
Giving almost 100 pts!!

Answer 1

Answer:

2cis(20°)

Step-by-step explanation:

we are given that

$\displaystyle \rm z = 10cis ({30}^{ \circ} )$

$\displaystyle \rm w = 5cis ({10}^{ \circ} )$

We want to find z/w . To do so, divide 10cis(30°) by w = 5cis(10°) which yields:

$\displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )}$

recall that,

$\displaystyle \rm \frac{ r_{1} cis ({ { \theta}_{1}} )}{ r_{2}cis( { \theta}_{2})} = \frac{ r_{1} }{ r_{2} } cis({ \theta}_{1} - { \theta}_{2})$

consider,

• ${ r}_{1} \implies 10$
• ${ r}_{2} \implies 5$
• ${ \theta}_{1} \implies {30}^{ \circ}$
• ${ \theta}_{2} \implies {10}^{ \circ}$

Therefore, utilizing the formula yields:

$\displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )} \\ \implies \rm\frac{ z}{w} = \dfrac{10}{5} cis( {30}^{ \circ} - {10}^{ \circ} ) \\ \implies \rm \dfrac{z}{w} = \boxed{ \rm2cis( {20}^{ \circ} )}$

and we're done!

NB: cis(x) is also known as cos(x)+i×sin(x)