How solve in complex plane equation z+|z|=8-4i?

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The equation z + |z| = 8 - 4i has to be solved.

If z = a + i*b, |z| = `sqrt(a^2 + b^2)`

`a + i*b + sqrt(a^2 + b^2) = 8 - 4i`

=> b = -4 and `a + sqrt(a^2 + b^2) = 8`

`a +sqrt(a^2 + 16) = 8 `

=> `64 + a^2 - 16a = a^2 + 16`

=> 16a = 48

=> a = 3

The complex number is 3 - 4i

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