I think it is easier to multiple (5-7i) (a+bi) and set the real part of the result equal to 148 and the imaginary part equal to zero. Then you will have a set of 2 linear equations with 2 unknowns, a and b. Simply solve those. Perhaps this takes a little bit longer, but not much.

## Comments (2)

I got the conjugation, but the doubling was troubling.

I think it is easier to multiple (5-7i) (a+bi) and set the real part of the result equal to 148 and the imaginary part equal to zero. Then you will have a set of 2 linear equations with 2 unknowns, a and b. Simply solve those. Perhaps this takes a little bit longer, but not much.