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-9\left(-9\right)-9\left(-i\right)-9i-i^{2}
Multiply complex numbers -9+i and -9-i like you multiply binomials.
-9\left(-9\right)-9\left(-i\right)-9i-\left(-1\right)
By definition, i^{2} is -1.
81+9i-9i+1
Do the multiplications.
81+1+\left(9-9\right)i
Combine the real and imaginary parts.
82
Do the additions.
Re(-9\left(-9\right)-9\left(-i\right)-9i-i^{2})
Multiply complex numbers -9+i and -9-i like you multiply binomials.
Re(-9\left(-9\right)-9\left(-i\right)-9i-\left(-1\right))
By definition, i^{2} is -1.
Re(81+9i-9i+1)
Do the multiplications in -9\left(-9\right)-9\left(-i\right)-9i-\left(-1\right).
Re(81+1+\left(9-9\right)i)
Combine the real and imaginary parts in 81+9i-9i+1.
Re(82)
Do the additions in 81+1+\left(9-9\right)i.
82
The real part of 82 is 82.