Question

3+2i/-2+i
Please solve this...​

Answer 1

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

Given complex number is

$\rm \longmapsto\:\dfrac{3 + 2i}{ - 2 + i}$

So, on rationalizing the denominator, we get

$\rm \:  =  \: \dfrac{3 + 2i}{ - 2 + i} \times \dfrac{ - 2 - i}{ - 2 - i}$

$\rm \:  =  \: \dfrac{ - 6 - 3i - 4i - {2i}^{2} }{ {( - 2)}^{2} - {i}^{2} }$

We know,

$\rm \red\longmapsto\:\tt{ {i}^{2} \: = \: - \: 1 \: }$

So, using this, we get

$\rm \:  =  \: \dfrac{ - 6 - 7i - 2( - 1) }{ 4 - ( - 1)}$

$\rm \:  =  \: \dfrac{ - 6 - 7i + 2}{ 4 + 1}$

$\rm \:  =  \: \dfrac{ - 4 - 7i }{5}$

$\rm \:  =  \: - \dfrac{4}{5} - \dfrac{7}{5} i$