Question

Find a and b such that -3ai-(-1 - i) b =3a - 2bi

Answer 1

Let us find $a$ and $b$ such that $-3ai-(-1 - i) b =3a - 2bi.$ It follows that $-3ai+b+bi =3a - 2bi,$ and hence $b+(b-3a)i =3a - 2bi$. Taking into account that two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal, we conclude that  $b=3a, b-3a =- 2b.$ Then $b=3a$ and $3b=3a.$ We conclude that $b=3b,$ which is equivalent to $2b=0,$ and hence $b=0$. It follows that $a=b=0.$

Answer: $a=0,b=0.$