Solve the equation in z : 2z+6i = z/2i+5i-7.

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We have to solve 2z + 6i = z/2i + 5i - 7

2z + 6i = z/2i + 5i - 7

=> 2z - z/ 2i = -i - 7

=> (2z*2i - z) / 2i = (-i - 7)

=> z( 4i - 1)/2i = (-i - 7)

=> z = (-i - 7) * 2i / ( 4i - 1)

=> z = (-2i^2 - 14i) / (4i - 1)

=> z = (2 - 14i)(4i + 1) / [(4i)^2 - (1)^2]

=> z = (8i + 56 + 2 - 14i) / (-16 - 1)

=> z = (58 - 6i)/ -17

=> z = -58/17 + 6i/17

The required result is z = -58/17 + 6i/17

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