a2linetagadaW

2021-09-21

Divide

$\frac{3+2i}{5-i}$

faldduE

Skilled2021-09-22Added 109 answers

Step 1

Given is$\frac{3+2i}{5-i}$

Step 2

Apply complex arithmetic rule:$\frac{a+bi}{c+di}=\frac{(a+bi)}{(c+di)}\times \frac{(c-di)}{(c-di)}$

Step 3

$\frac{3+2i}{5-i}\times \frac{5+i}{5+i}$

$\frac{(3+2i)(5+i)}{(5+i)(5-i)}[\because (a+b)(a-b)={a}^{2}-{b}^{2}]$

$\frac{(15+3i+10i+2{i}^{2})}{({5}^{2}-{i}^{2})}[\because {i}^{2}=-1]$

$\frac{(15+13i-2)}{({5}^{2}-(-1))}$

$\frac{(13+13i)}{(25+1)}$

$\frac{(13+13i)}{\left(26\right)}$

$\frac{13}{26}+\frac{13}{26}i$

$\frac{1}{2}(1+i)$

Step 4

The required answer is

$\frac{1}{2}(1+i)$

Given is

Step 2

Apply complex arithmetic rule:

Step 3

Step 4

The required answer is

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