Question

How do you divide `4+2i div 3-i`?

Answer 1

The result is `1+i`

Explanation:

To perform the division of complex numbers you have to expand the fraction by the complex conjugate of the denominator. After doing this you get a real number in the denominator.

`(4+2i)/(3-i)=((4+2i)(3+i))/((3-i)(3+i))=(10+10i)/10=1+i`

Answer 2

`1+i`

Explanation:

`(4+2i)/(3-i)`
Multiply and divide by the conjugate of the expression present in denominator i.e `3+i`.
`implies (4+2i)/(3-i)=(4+2i)/(3-i)*(3+i)/(3+i)=(12+4i+6i+2i^2)/((3)^2-(i)^2)`
`=(12+10i-2)/(9-(-1))=(10+10i)/(9+1)=(10(1+i))/10=1+i`
Hence the answer is `1+i`.