Evaluate
-18
Real Part
-18
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3\left(-3\right)+3\times \left(3i\right)+3i\left(-3\right)+3\times 3i^{2}
Multiply complex numbers 3+3i and -3+3i like you multiply binomials.
3\left(-3\right)+3\times \left(3i\right)+3i\left(-3\right)+3\times 3\left(-1\right)
By definition, i^{2} is -1.
-9+9i-9i-9
Do the multiplications.
-9-9+\left(9-9\right)i
Combine the real and imaginary parts.
-18
Do the additions.
Re(3\left(-3\right)+3\times \left(3i\right)+3i\left(-3\right)+3\times 3i^{2})
Multiply complex numbers 3+3i and -3+3i like you multiply binomials.
Re(3\left(-3\right)+3\times \left(3i\right)+3i\left(-3\right)+3\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(-9+9i-9i-9)
Do the multiplications in 3\left(-3\right)+3\times \left(3i\right)+3i\left(-3\right)+3\times 3\left(-1\right).
Re(-9-9+\left(9-9\right)i)
Combine the real and imaginary parts in -9+9i-9i-9.
Re(-18)
Do the additions in -9-9+\left(9-9\right)i.
-18
The real part of -18 is -18.
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Limits
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