Evaluate
-4-12i
Real Part
-4
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1\times 4+1\times \left(-4i\right)-2i\times 4-2\left(-4\right)i^{2}
Multiply complex numbers 1-2i and 4-4i like you multiply binomials.
1\times 4+1\times \left(-4i\right)-2i\times 4-2\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
4-4i-8i-8
Do the multiplications.
4-8+\left(-4-8\right)i
Combine the real and imaginary parts.
-4-12i
Do the additions.
Re(1\times 4+1\times \left(-4i\right)-2i\times 4-2\left(-4\right)i^{2})
Multiply complex numbers 1-2i and 4-4i like you multiply binomials.
Re(1\times 4+1\times \left(-4i\right)-2i\times 4-2\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(4-4i-8i-8)
Do the multiplications in 1\times 4+1\times \left(-4i\right)-2i\times 4-2\left(-4\right)\left(-1\right).
Re(4-8+\left(-4-8\right)i)
Combine the real and imaginary parts in 4-4i-8i-8.
Re(-4-12i)
Do the additions in 4-8+\left(-4-8\right)i.
-4
The real part of -4-12i is -4.
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