Question

If a-bi/a+bi=1+i/1-i then,prove a+b=0

Answer 1

Answer:

a+b=0

Step-by-step explanation:

$\textsf{Given:}$

$\displaystyle\mathsf{\frac{a-ib}{a+ib}=\frac{1+i}{1-i}}$

$\displaystyle\mathsf{\frac{a-ib}{a+ib}=\frac{1+i}{1-i}}$

$\implies\mathsf{(a-ib)(1-i)=(a+ib)(1+i)}$

$\implies\mathsf{a-ai-ib+i^2b=a+ai+ib+i^2b}$

$\textsf{Using,\;\; i^2=-1 }$

$\implies\mathsf{(a-b)-i(a+b)=(a-b)+i(a+b)}$

$\textsf{Equating corresponding real and imaginary parts on both sides, we get}$

$\implies\mathsf{-(a+b)=a+b}$

$\implies\mathsf{-2(a+b)=0}$

$\implies\boxed{\mathsf{a+b=0}}$