Determine the complex number z if (z'+7i)/z=6?

Let the complex number z = x + iy. The complement of z ,
z' = x - iy.

As (z' + 7i)/z =
6

=> ( x - iy + 7i)/ ( x + iy) =
6

=> x - iy + 7i = 6*(x +
iy)

=> x - iy + 7i = 6x +
6*i*y

=> x - 6x - iy - 6iy + 7i =
0

=> -5x - 7iy = -7i +
0

Equate the real and complex
parts

=> -5x =
0

=> x = 0

-7iy =
-7i

=> y =
1

Therefore the complex number z is
i.

We can see : (-i + 7i)/i = 6i/i =
6.