Principles of Mathematics

Polar Complex Number Division

Division in Polar form can be done through reverting back the polar term to its rectangular form. After converting, complex conjugate is then applied to solve the division. This is one method. There is however another method in Polar form.

Polar Division Formula:  A ÐK⁰  / B ÐY⁰ = (A/B) ÐK- Y ⁰.

Example 1:   6 Ð40⁰  / 2 Ð30⁰  

Solution:  (6 /2 )  Ð40 - 30⁰  ==> 3 Ð10⁰.

Example 2:   4 Ð-50⁰  / 2 Ð30⁰  

Solution:  (4 /2 )  Ð-50 - 30⁰  ==> 2 Ð-80⁰.

This is a faster method if the final answer is in the polar form. In the case where the final answer has to be in rectangular form, judgement to which method (polar or conjugate) is suitable has to be performed. However, whatever technique you use, the answer will be the same except one will have more steps.