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

1 Answer
May 22, 2017

#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#