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What is complex number z if z+3i=6 conjugate z?

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varka | Student, Undergraduate | eNoter

Posted July 11, 2013 at 3:19 PM via web

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What is complex number z if z+3i=6 conjugate z?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 11, 2013 at 3:31 PM (Answer #1)

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You need to use the algebraic form of complex number `z = x + y*i` and its conjugate `bar z = x - y*i` , such that:

`z + 3i = 6bar z => x + y*i + 3i = 6(x - y*i)`

`x + y*i + 3i = 6x - 6y*i => x - 6x + i*(y + 3 + 6y) = 0`

`-5x + i*(7y + 3) = 0 + 0*i`

Equating the real parts and imaginary parts yields:

`{(-5x = 0),(7y + 3 = 0):} => {(x = 0),(y = -3/7):}`

Hence, evaluating the complex number z, under the given conditions, yields `z = 0 - (3/7)*i.`

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