Evaluate
-65+72i
Real Part
-65
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4\times 4+4\times \left(9i\right)+9i\times 4+9\times 9i^{2}
Multiply complex numbers 4+9i and 4+9i like you multiply binomials.
4\times 4+4\times \left(9i\right)+9i\times 4+9\times 9\left(-1\right)
By definition, i^{2} is -1.
16+36i+36i-81
Do the multiplications.
16-81+\left(36+36\right)i
Combine the real and imaginary parts.
-65+72i
Do the additions.
Re(4\times 4+4\times \left(9i\right)+9i\times 4+9\times 9i^{2})
Multiply complex numbers 4+9i and 4+9i like you multiply binomials.
Re(4\times 4+4\times \left(9i\right)+9i\times 4+9\times 9\left(-1\right))
By definition, i^{2} is -1.
Re(16+36i+36i-81)
Do the multiplications in 4\times 4+4\times \left(9i\right)+9i\times 4+9\times 9\left(-1\right).
Re(16-81+\left(36+36\right)i)
Combine the real and imaginary parts in 16+36i+36i-81.
Re(-65+72i)
Do the additions in 16-81+\left(36+36\right)i.
-65
The real part of -65+72i is -65.
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