It looks to me like you started with \(\displaystyle \frac{15.497+ j0.888}{30+ j25}\)
and the multiplied both numerator and denominator by \(\displaystyle 30- j25\).
Of course multiplying both numerator and denominator of any fraction by the same thing doesn't change the value of the fraction! But it is standard to do that to fractions of complex numbers. We are multiplying numerator and denominator by the complex conjugate of the denominator because \(\displaystyle (c+ jd)(c- jd)= c^2- jcd+ jcd- j^2d^2= c^2+ d^2\), a positive real number. Note that -jcd+ jcd cancel while \(\displaystyle j^2d^2= -d^2\).
In this particular problem, the denominator will be \(\displaystyle (30+ j25)(30- j25)= 30^2+ 25^2\), a real number. So the problem is now to multiply \(\displaystyle (15.497+ j0.888)(30- j25)= (15.497)(30)- j(15.497)(25)+ j(0.888)(30)+ (0.888)(25)\) and then divide by the real number denomimator.