Question

2. Describe how to use the conjugate to divide 2 − i by 3 + 2i, and then find the quotient.

Answer 1

`(4)/(13)-(7)/(13)i`

Explanation:

`(2-i)/(3+2i)`

Multiply and divide by the conjugate.

The conjugate is the denominator with the sign of the complex number the opposite of the denominator.

`(2-i)/(3+2i)(3-2i)/(3-2i)\\ =(2* (3-2i)-i* (3-2i))/(3^2-(2i)^2)\\ =(6-4i-3i+2i^2)/(9+4)\\ =(4-7i)/(13)\\ =(4)/(13)-(7)/(13)i`

Quotient =
`(4)/(13)-(7)/(13)i`