As z is a complex number let it be x + yi. z' = x - yi.

If z/2 + 3=z'/3 - 2

=> (x + yi)/2 + 3 = (x - yi)/3 - 2

=> (x + yi)/2 - (x -yi)/3 = -5

=> x/2 - x/3 - i(...

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As z is a complex number let it be x + yi. z' = x - yi.

If z/2 + 3=z'/3 - 2

=> (x + yi)/2 + 3 = (x - yi)/3 - 2

=> (x + yi)/2 - (x -yi)/3 = -5

=> x/2 - x/3 - i( y/2 - y/3) = -5

=> x/2 - x/3 = -5

=> (3x - 2x)/6 = -5

=> x = -30

y = 0 as there is no imaginary component on the opposite side.

Therefore **z = -30**