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-4\times 2-4\left(-i\right)+3i\times 2+3\left(-1\right)i^{2}
Multiply complex numbers -4+3i and 2-i like you multiply binomials.
-4\times 2-4\left(-i\right)+3i\times 2+3\left(-1\right)\left(-1\right)
By definition, i^{2} is -1.
-8+4i+6i+3
Do the multiplications.
-8+3+\left(4+6\right)i
Combine the real and imaginary parts.
-5+10i
Do the additions.
Re(-4\times 2-4\left(-i\right)+3i\times 2+3\left(-1\right)i^{2})
Multiply complex numbers -4+3i and 2-i like you multiply binomials.
Re(-4\times 2-4\left(-i\right)+3i\times 2+3\left(-1\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-8+4i+6i+3)
Do the multiplications in -4\times 2-4\left(-i\right)+3i\times 2+3\left(-1\right)\left(-1\right).
Re(-8+3+\left(4+6\right)i)
Combine the real and imaginary parts in -8+4i+6i+3.
Re(-5+10i)
Do the additions in -8+3+\left(4+6\right)i.
-5
The real part of -5+10i is -5.