How do you divide ( -7i-3) / ( 9 i -4 )−7i−39i−4 in trigonometric form?

1 Answer
Jacob T.
May 22, 2017

sqrt(5626)/97*cis(132.84^o)=-51/97+55/97*i√562697⋅cis(132.84o)=−5197+5597⋅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)−7⋅i−3=√58⋅cis(−113.20o)
The denominator in polar form: 9*i-4=sqrt(97)*cis(113.96^o)9⋅i−4=√97⋅cis(113.96o)

Then evaluate the division:
(-7i-3)/(9i-4)−7i−39i−4
=(sqrt(58)/sqrt(97))*cis(-113.20^o-113.96^o)=(√58√97)⋅cis(−113.20o−113.96o)
=sqrt(5626)/97*cis(132.84^o)=√562697⋅cis(132.84o)

Convert back to rectangular form:
=-51/97+55/97*i=−5197+5597⋅i

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