z* is the complex conjugate of z therefore z* = x - yi. So 16 + 32i = 5(x + yi)-3(x - yi), real: 16 = 5x - 3x => 16=2x => x=8, imaginary: 32 = 5y + 3y => 32 = 8y => y=4, therefore z = 8 + 4i.
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