Evaluate
-12-21i
Real Part
-12
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2\times 3+2\times \left(-6i\right)-3i\times 3-3\left(-6\right)i^{2}
Multiply complex numbers 2-3i and 3-6i like you multiply binomials.
2\times 3+2\times \left(-6i\right)-3i\times 3-3\left(-6\right)\left(-1\right)
By definition, i^{2} is -1.
6-12i-9i-18
Do the multiplications.
6-18+\left(-12-9\right)i
Combine the real and imaginary parts.
-12-21i
Do the additions.
Re(2\times 3+2\times \left(-6i\right)-3i\times 3-3\left(-6\right)i^{2})
Multiply complex numbers 2-3i and 3-6i like you multiply binomials.
Re(2\times 3+2\times \left(-6i\right)-3i\times 3-3\left(-6\right)\left(-1\right))
By definition, i^{2} is -1.
Re(6-12i-9i-18)
Do the multiplications in 2\times 3+2\times \left(-6i\right)-3i\times 3-3\left(-6\right)\left(-1\right).
Re(6-18+\left(-12-9\right)i)
Combine the real and imaginary parts in 6-12i-9i-18.
Re(-12-21i)
Do the additions in 6-18+\left(-12-9\right)i.
-12
The real part of -12-21i is -12.
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