Evaluate
-3-33i
Real Part
-3
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-5\left(-3\right)-5\times \left(3i\right)+6i\left(-3\right)+6\times 3i^{2}
Multiply complex numbers -5+6i and -3+3i like you multiply binomials.
-5\left(-3\right)-5\times \left(3i\right)+6i\left(-3\right)+6\times 3\left(-1\right)
By definition, i^{2} is -1.
15-15i-18i-18
Do the multiplications.
15-18+\left(-15-18\right)i
Combine the real and imaginary parts.
-3-33i
Do the additions.
Re(-5\left(-3\right)-5\times \left(3i\right)+6i\left(-3\right)+6\times 3i^{2})
Multiply complex numbers -5+6i and -3+3i like you multiply binomials.
Re(-5\left(-3\right)-5\times \left(3i\right)+6i\left(-3\right)+6\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(15-15i-18i-18)
Do the multiplications in -5\left(-3\right)-5\times \left(3i\right)+6i\left(-3\right)+6\times 3\left(-1\right).
Re(15-18+\left(-15-18\right)i)
Combine the real and imaginary parts in 15-15i-18i-18.
Re(-3-33i)
Do the additions in 15-18+\left(-15-18\right)i.
-3
The real part of -3-33i is -3.
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