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Complex numbers.Find the polar form of the complex number 7–5i.

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portoruj | Student, Grade 10 | eNoter

Posted May 11, 2011 at 2:07 AM via web

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Complex numbers.

Find the polar form of the complex number 7–5i.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted February 25, 2013 at 6:21 PM (Answer #3)

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You need to remember what is the polar form of a complex number, such that:

`z = sqrt(a^2 + b^2)(cos alpha + i*sin alpha)`

You need to convert the algebraic form `z = a + b*i` into polar form, hence, finding `a =7` and `b = -5` , yields:

`sqrt(a^2 + b^2) = sqrt(49 + 25) => sqrt(a^2 + b^2) = sqrt 74`

`tan alpha = b/a => tan alpha = -5/7 => alpha = tan^(-1)(-5/7) => alpha = -tan^(-1)(5/7) `

`z = sqrt 74(cos(tan^(-1)(5/7)) - i*sin(tan^(-1)(5/7)))`

Hence, evaluating the polar form of the given complex number, yields `z = sqrt 74(cos(tan^(-1)(5/7)) - i*sin(tan^(-1)(5/7))).`

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