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

2cis(20°)

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 ( z)/(w) = \frac{10cis ({30}^( \circ) )}{5cis( {10}^( \circ) )}`

recall that,

`\displaystyle \rm \frac{ r_(1) cis ({ { \theta}_(1)} )}{ r_(2)cis( { \theta}_(2))} = ( 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 ( z)/(w) = \frac{10cis ({30}^( \circ) )}{5cis( {10}^( \circ) )} \\ \implies \rm( z)/(w) = (10)/(5) cis( {30}^( \circ) - {10}^( \circ) ) \\ \implies \rm (z)/(w) = \boxed{ \rm2cis( {20}^( \circ) )}`

and we're done!

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