Evaluate
-24-138i
Real Part
-24
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12\times 3+12\times \left(-10i\right)-6i\times 3-6\left(-10\right)i^{2}
Multiply complex numbers 12-6i and 3-10i like you multiply binomials.
12\times 3+12\times \left(-10i\right)-6i\times 3-6\left(-10\right)\left(-1\right)
By definition, i^{2} is -1.
36-120i-18i-60
Do the multiplications.
36-60+\left(-120-18\right)i
Combine the real and imaginary parts.
-24-138i
Do the additions.
Re(12\times 3+12\times \left(-10i\right)-6i\times 3-6\left(-10\right)i^{2})
Multiply complex numbers 12-6i and 3-10i like you multiply binomials.
Re(12\times 3+12\times \left(-10i\right)-6i\times 3-6\left(-10\right)\left(-1\right))
By definition, i^{2} is -1.
Re(36-120i-18i-60)
Do the multiplications in 12\times 3+12\times \left(-10i\right)-6i\times 3-6\left(-10\right)\left(-1\right).
Re(36-60+\left(-120-18\right)i)
Combine the real and imaginary parts in 36-120i-18i-60.
Re(-24-138i)
Do the additions in 36-60+\left(-120-18\right)i.
-24
The real part of -24-138i is -24.
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