Question

3+2i/-2+i
Please solve this...​

Answer 1

`\large\underline{\sf{Solution-}}`

Given complex number is

`\rm \longmapsto\:(3 + 2i)/( - 2 + i)`

So, on rationalizing the denominator, we get

`\rm \:  =  \: (3 + 2i)/( - 2 + i) * ( - 2 - i)/( - 2 - i)`

`\rm \:  =  \: \frac{ - 6 - 3i - 4i - {2i}^(2) }{ {( - 2)}^(2) - {i}^(2) }`

We know,

`\rm \red\longmapsto\:\tt{ {i}^(2) \: = \: - \: 1 \: } \\`

So, using this, we get

`\rm \:  =  \: ( - 6 - 7i - 2( - 1) )/( 4 - ( - 1))`

`\rm \:  =  \: ( - 6 - 7i + 2)/( 4 + 1)`

`\rm \:  =  \: ( - 4 - 7i )/(5)`

`\rm \:  =  \: - (4)/(5) - (7)/(5) i`