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

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

then x =1(6+5i)2.
Now,we have to rationalize in order to obtain a simple expression.

i.e, x = 1(6+5i)2×(6-5i)2(6-5i)2
  =36 + 25i2 -60i(36-25i2)2  {using (a+b)(a-b) = (a2-b2) }
  =36-25-60i(36+25)2=11-60i612=11-60i3721,
which is the required multiplicative inverse of the given problem.

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