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I'm having trouble with this kind of question.

Solve for z, and give your answer in the form a+bi.

(z-3+2i)/z = -2+3i

Whenever I manage to isolate z, the answer I get ends up being incorrect.

All help is appreciated.

Thanks.

  • 2
    What is your answer? What is the correct result? You should give more details. – 2017-02-27
  • 0
    For a willing Reader to identify what you are doing wrong, you must share what you did to "isolate $z$". I can imagine a couple of good first steps. – 2017-02-27

2 Answers 2

1

$$\frac{z-3+2i}z=-2+3i\iff z-3+2i=-2z+3zi\implies (3-3i)z=3-2i\implies$$

$$z=\frac{3-2i}{3-3i}\cdot\frac{3+3i}{3+3i}=\frac{15+3i}{18}=\frac56+\frac16i=\frac16(5+i)$$

1

Multiplying both sides by $z$, we get

$$z-3+2i=-2z+3iz$$

and

$$-3+2i=3z(-1+i)$$

which gives

$$z=\frac{-3+2i}{3(-1+i)}$$

$$=\frac{(-3+2i)(-1-i)}{6}$$

$$=\frac{1}{6}(5+i).$$