Question

How do you divide `( -7i-3) / ( 9 i -4 )` in trigonometric form?

Answer 1

`sqrt(5626)/97*cis(132.84^o)=-51/97+55/97*i`

Explanation:

To evaluate the division in trig. Form, first you convert the numerator and denominator to polar form:
The numerator in polar form: `-7*i-3=sqrt(58)*cis(-113.20^o)`
The denominator in polar form: `9*i-4=sqrt(97)*cis(113.96^o)`

Then evaluate the division:
`(-7i-3)/(9i-4)`
`=(sqrt(58)/sqrt(97))*cis(-113.20^o-113.96^o)`
`=sqrt(5626)/97*cis(132.84^o)`

Convert back to rectangular form:
`=-51/97+55/97*i`