Question 78176
{{{(3-i)^-2}}} Start with the given expression
{{{1/(3-i)^2}}} Invert
{{{1/(9-6i+i^2)}}} Foil
{{{1/(9-6i+-1)}}} replace {{{i^2}}} with (-1) Since {{{i=sqrt(-1)}}} {{{i^2=-1}}}
{{{1/(8-6i)}}}  Combine like terms
{{{(1/(8-6i))((8+6i)/(8+6i))}}} Multiply the numerator and denominator by the complex conjugate {{{8+6i}}} this will rationalize the denominator (ie it will get rid of the i term in the denominator)
{{{(8+6i)/((8-6i)(8+6i))}}} Multiply
{{{(8+6i)/(64+cross(48i-48i)-36i^2)}}} Foil
{{{(8+6i)/(64-36i^2)}}} Combine like terms
{{{(8+6i)/(64-36(-1))}}} Replace {{{i^2}}} with (-1)
{{{(8+6i)/(64+36)}}} Multiply -36 by -1
{{{(8+6i)/100}}}Combine like terms
{{{2(4+3i)/100}}} Factor out a 2
{{{(4+3i)/50}}} Divide