what z=? if (cojugate z+7i)/z=6?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should remeber that complex conjugates possess the same real parts and opposite imaginary parts such that:

`z = a + b*i =gt bar z = a - b*i`

The problem provides the equation that relates the complex conjugates, hence, I suggest to you to substitute `a + b*i`  for z and a - b*i for `bar z`  such that:

`(a - b*i + 7*i)/(a+ b*i)= 6`

Factoring out `i`  to numerator yields:

`a + i(7 - b) = 6a + 6bi =gt -5a + i*(7 - b - 6b) = 0`

`-5a + i*(7 - 7b) = 0`

You need to write the right side as a complex number such that:

`-5a = 0 =gt a = 0`

`7 - 7b = 0 =gt 7b = 7 =gt b = 1`

Hence, evaluating the complex number z, under the given conditions, yields `z = i.`

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