Question

1-4i/3+2i how do I solve this

Answer 1

To divide a complex a+ib by a complex number c+id we have to multiply the numerator and denominator by the complex conjugate of the denominator of the original fraction; after that we make the operations.

With this in mind in this case we have:

`\begin{gathered} (1-4i)/(3+2i)\cdot(3-2i)/(3-2i)=(3-2i-12i+8i^2)/(9-6i+6i-4i^2) \\ =(3-14i-8)/(9+4) \\ =(-5-14i)/(13) \\ =-(5)/(13)-(14)/(13)i \end{gathered}`

Therefore the result of the division given is:

`-(5)/(13)-(14)/(13)i`