Evaluate
-24+3i
Real Part
-24
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\left(2\times 3+3i\right)\left(-3+2i\right)
Multiply 2+i times 3.
\left(6+3i\right)\left(-3+2i\right)
Do the multiplications.
6\left(-3\right)+6\times \left(2i\right)+3i\left(-3\right)+3\times 2i^{2}
Multiply complex numbers 6+3i and -3+2i like you multiply binomials.
6\left(-3\right)+6\times \left(2i\right)+3i\left(-3\right)+3\times 2\left(-1\right)
By definition, i^{2} is -1.
-18+12i-9i-6
Do the multiplications.
-18-6+\left(12-9\right)i
Combine the real and imaginary parts.
-24+3i
Do the additions.
Re(\left(2\times 3+3i\right)\left(-3+2i\right))
Multiply 2+i times 3.
Re(\left(6+3i\right)\left(-3+2i\right))
Do the multiplications in 2\times 3+3i.
Re(6\left(-3\right)+6\times \left(2i\right)+3i\left(-3\right)+3\times 2i^{2})
Multiply complex numbers 6+3i and -3+2i like you multiply binomials.
Re(6\left(-3\right)+6\times \left(2i\right)+3i\left(-3\right)+3\times 2\left(-1\right))
By definition, i^{2} is -1.
Re(-18+12i-9i-6)
Do the multiplications in 6\left(-3\right)+6\times \left(2i\right)+3i\left(-3\right)+3\times 2\left(-1\right).
Re(-18-6+\left(12-9\right)i)
Combine the real and imaginary parts in -18+12i-9i-6.
Re(-24+3i)
Do the additions in -18-6+\left(12-9\right)i.
-24
The real part of -24+3i is -24.
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