Question

(1+i) ^3/(2+i) (1+2i)

Answer 1

Step-by-step explanation:

We have,

$\frac{(1 + i)^{3} }{(2 + i)(1 + 2i)}$

$= \frac{ {(1)}^{3} + ( i)^{3} + 3. {(1)}^{2}.i + 3.1. {(i)}^{2} }{(2 + 4i + i + 2 {(i)}^{2}) }$

$= \frac{ 1 - i + 3i - 3 }{2 + 5i - 2 }$

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

$= \frac{( - 2 + 2i ) i }{ 5i .i }$

$= \frac{ - 2i + 2.i^{2} }{ 5.i^{2} }$

$= \frac{ - 2i - 2 }{ - 5 }$

$= \frac{ 2i + 2 }{ 5 }$

$= \frac{ 2 }{ 5 } + \frac{2}{5}i$