Question

Simplify : ilog((x-i)/(x+i))

Answer 1

Answer:

$=2ilog(x-i)-ilog(x^2+1)$

Step-by-step explanation:

Given:

$ilog(\frac{x-i}{x+i} )\\ \\=ilog(\frac{x-i}{x+i}*\frac{x-i}{x-i})\\ \\=ilog(\frac{(x-i)^2}{x^2+1})\\ \\=i[log(x-i)^2-log(x^2+1)]\\ \\=2ilog(x-i)-ilog(x^2+1)$

Answer 2

Thanks for the question!

It is definitely a very interesting question to solve and do some brainstorming.

**************************************************

ilog(x-i/x+i.x-i/x-i)

ilog{(x-i)2/x2-i2)}

ilog{(x-i)2/x2+1)}.           (i2=-1)

i{log(x-i)2-log(x2+1)}.      (loga/b=loga-logb)

i{2log(x-i)-log(x2+1)}.       ( logab=bloga)

2ilog(x-i)-ilog(x2+1)

**************************************************

Hope it helps and solves your query!!