Question 131877
Simplify:
{{{(3-i)/(1+i)}}} First, rationalise the denominator by multiplying by its conjugate, {{{(1-i)}}}
{{{(3-i)(1-i)/(1+i)(1-i)}}} Simplify.
{{{(3-4i+i^2)/(1-i^2)}}} Substitute:{{{i^2 = -1}}}
{{{(3-4i+(-1))/(1-(-1))}}} Simplify.
{{{(2-4i)/(2)}}} Factor 2 from the numerator.
{{{2(1-2i)/2}}} Cancel the 2's to leave you with:
{{{1-2i}}}, so...
{{{(3-i)/(1+i) = 1-2i}}}