Question 120434
{{{(6 + 5i)^-1}}} Start with the given expression




{{{1/(6 + 5i)}}} Rewrite the expression as {{{1/(6 + 5i)}}}. Remember, {{{x^-2=1/x^2}}}


*[Tex \LARGE \left(\frac{1}{6+5i}\right)\left(\frac{6-5i}{6-5i}\right)] Multiply the fraction by *[Tex \LARGE \frac{6-5i}{6-5i}]


*[Tex \LARGE \frac{6-5i}{61}] Foil and Multiply



*[Tex \LARGE \frac{6}{61}-\frac{5}{61}i] Break up the fraction. So it is now in {{{a+bi}}} form where {{{a=6/61}}} and {{{b=-5/61}}}



So *[Tex \LARGE \left(6+5i\right)^{-1}] simplifies to  *[Tex \LARGE \frac{6}{61}-\frac{5}{61}i] 



In other words, *[Tex \LARGE \left(6+5i\right)^{-1}=\frac{6}{61}-\frac{5}{61}i]