How do you divide 7−4i3+2i in trigonometric form?

1 Answer
Shwetank Mauria
Mar 2, 2016

√5×ei(α−β), where α=tan−1(−47) and β=tan−1(23)

Explanation:

(a+bi) an be written in as √a2+b2ei(tan−1(ba))

Hence, (7−4i)=√72+42(eitan−1(−47))=√65eitan−1(−47)

Similarly, (3+2i)=√32+22(eitan−1(23))=√13eitan−1(23)

Hence 7−4i3+2i=√65eitan−1(−47)√13eitan−1(23)

or √5×ei(tan−1(−47))−(tan−1(23)) or

√5×ei(α−β), where α=tan−1(−47) and β=tan−1(23)

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