Find the multiplicative inverse of (6+5i)2

Let x be the multiplicative inverse of (6+5i)2 .

then x =$\frac{1}{\left(6+5i{\right)}^{2}}$.
Now,we have to rationalize in order to obtain a simple expression.

i.e, x = $\frac{1}{\left(6+5i{\right)}^{2}}×\frac{\left(6-5i{\right)}^{2}}{\left(6-5i{\right)}^{2}}$
=  {using (a+b)(a-b) = (${a}^{2}-{b}^{2}$) }
=$\frac{36-25-60i}{\left(36+25{\right)}^{2}}=\frac{11-60i}{{61}^{2}}=\frac{11-60i}{3721}$,
which is the required multiplicative inverse of the given problem.

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