Question

i/(2+i) +3\ ( 1+ 4i)​

Answer 1

$\huge\mathfrak{Answer}$

$\huge\sf{solution:}$

$\frac{i}{2 + i} + \frac{3}{1 + 4i}$

first, do multipicative inverse

$\implies$$\frac{ i \times (2 - i)}{(2 + i) \times (2 - i)} + \frac{3 \times (1 - 4i)}{(1 + 4i)(1 - 4i)}$

$\implies$$\frac{ 2i - {i}^{2} }{4 - {i}^{2} } + \frac{3 - 12i}{1 - {4i}^{2} }$

$\implies$$\frac{ 2i + 1}{4 + 1} + \frac{3 - 12i}{1 + 16}$

$\implies$$\frac{17(2 - i) + 5(3 - 12i)}{85}$

$\implies$$\frac{34 + 15 - 17i - 60i}{85}$

$\implies$$\frac{ 49 - 77i}{85}$

$\implies$$\frac{49}{85} - \frac{77i}{85}$