Evaluate
28-16i
Real Part
28
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\left(2\times 4+2\times \left(2i\right)\right)\left(2-3i\right)
Multiply 2 times 4+2i.
\left(8+4i\right)\left(2-3i\right)
Do the multiplications.
8\times 2+8\times \left(-3i\right)+4i\times 2+4\left(-3\right)i^{2}
Multiply complex numbers 8+4i and 2-3i like you multiply binomials.
8\times 2+8\times \left(-3i\right)+4i\times 2+4\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
16-24i+8i+12
Do the multiplications.
16+12+\left(-24+8\right)i
Combine the real and imaginary parts.
28-16i
Do the additions.
Re(\left(2\times 4+2\times \left(2i\right)\right)\left(2-3i\right))
Multiply 2 times 4+2i.
Re(\left(8+4i\right)\left(2-3i\right))
Do the multiplications in 2\times 4+2\times \left(2i\right).
Re(8\times 2+8\times \left(-3i\right)+4i\times 2+4\left(-3\right)i^{2})
Multiply complex numbers 8+4i and 2-3i like you multiply binomials.
Re(8\times 2+8\times \left(-3i\right)+4i\times 2+4\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(16-24i+8i+12)
Do the multiplications in 8\times 2+8\times \left(-3i\right)+4i\times 2+4\left(-3\right)\left(-1\right).
Re(16+12+\left(-24+8\right)i)
Combine the real and imaginary parts in 16-24i+8i+12.
Re(28-16i)
Do the additions in 16+12+\left(-24+8\right)i.
28
The real part of 28-16i is 28.
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