Evaluate
85
Real Part
85
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9\times 9+9\times \left(-2i\right)+2i\times 9+2\left(-2\right)i^{2}
Multiply complex numbers 9+2i and 9-2i like you multiply binomials.
9\times 9+9\times \left(-2i\right)+2i\times 9+2\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
81-18i+18i+4
Do the multiplications.
81+4+\left(-18+18\right)i
Combine the real and imaginary parts.
85
Do the additions.
Re(9\times 9+9\times \left(-2i\right)+2i\times 9+2\left(-2\right)i^{2})
Multiply complex numbers 9+2i and 9-2i like you multiply binomials.
Re(9\times 9+9\times \left(-2i\right)+2i\times 9+2\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(81-18i+18i+4)
Do the multiplications in 9\times 9+9\times \left(-2i\right)+2i\times 9+2\left(-2\right)\left(-1\right).
Re(81+4+\left(-18+18\right)i)
Combine the real and imaginary parts in 81-18i+18i+4.
Re(85)
Do the additions in 81+4+\left(-18+18\right)i.
85
The real part of 85 is 85.
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