Question

if $( \frac{1 - i}{1 + i} ) {}^{36} = A + iB$ then find the value of A and B

Answer 1

$\bold{\huge{Hay!!}}$


$\bold{Dear\:user!!}$



$\bold{\underline{Question-}}$

if $( \frac{1 - i}{1 + i} ) {}^{36} = A + iB$ then find the value of A and B


$\bold{\underline{Answer-}}$


$\bold{Your\:answer\:is\:\:(A = 1 , B = 0)}$


$\bold{\underline{Explanation-}}$

$( \frac{1 - i}{1 + i} ) {}^{36} = A + iB \:$


$[ \frac{(1 - i)(1 - i)}{(1 + i)(1 - i)} ] {}^{36} = A + iB \\ \\ \\ \\ [ \frac{1 + {i}^{2} - 2i }{1 - {i}^{2} } ] {}^{36} = A + iB \\ \\ \\ \\ [ \frac{ - 2i}{1 + 1} ] {}^{36} = A + iB \\ \\ \\ \\ [ - i] {}^{36} = A + iB \\ \\ \\ \\ [ {( - i)}^{2} ] {}^{18} = A + iB \\ \\ \\ \\ [1] {}^{18} = A + iB \\ \\ \\ \\ 1 + 0i {}^{18} = A + iB \\ \\ \\ \\ A = 1 \: \: \: \: \: \: \: \: \: . \: \: \: \: \: \: \: \: \: B = 0$

Answer 2

Answer:

Step-by-step explanation:

A = 1 AND B= 0