Question

plz answer it guys l need help​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$i \: \sf{ \: is \: a \: complex \: number \: such \: that \: \: }$

${i}^{2} = - 1$

TO DETERMINE

Express

$\displaystyle \: { \bigg( \: \frac{1 + i}{1 - i} \bigg)}^{2}$

$\sf{Which \: is \: of \: the \: form \: a + ib}$

EVALUATION

Here

$\displaystyle \: { \bigg( \: \frac{1 + i}{1 - i} \bigg)}$

$= \displaystyle \: \frac{i}{i} { \bigg( \: \frac{1 + i}{1 - i} \bigg)}$

$= \displaystyle \: i { \bigg( \: \frac{1 + i}{i - {i}^{2} } \bigg)}$

$= \displaystyle \: i { \bigg( \: \frac{1 + i}{i + 1 } \bigg)}$

$= \displaystyle \: i { \bigg( \: \frac{1 + i}{1 + i } \bigg)}$

$= i$

Hence

$\displaystyle \: { \bigg( \: \frac{1 + i}{1 - i} \bigg)}^{2}$

$= {i}^{2}$

$= - 1$

$= - 1+ 0i$

$\sf{Which \: is \: of \: the \: form \: a + ib}$

$\sf{ \: Where \: \: a = - 1 \: \: and \: \: b = 0 \: }$