The step in converting this complex number to a + bi form is simply to multiply this complex number by its conjugate. See the solution below.
MTheultiply the expression by the conjugate of the denominator.
[tex]\frac{1}{6+5i}\times\frac{6-5i}{6-5i}[/tex][tex]\begin{gathered} =\frac{1(6-5i)}{6(6-5i)+5i(6-5i_{}} \\ =\frac{6-5i}{36-30i+30i-5i^2} \\ =\frac{6-5i}{36-5i^2} \\ i^2=-1 \\ =\frac{6-5i}{36-5(-1)} \\ =\frac{6-5i}{36+5} \\ =\frac{6-5i}{41} \\ =\frac{6}{41}-\frac{5}{41}i \end{gathered}[/tex]Therefore, its standard form is 6/41 - (5/41)i.
