Evaluate
32-4i
Real Part
32
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8\times 3+8\times \left(-2i\right)+4i\times 3+4\left(-2\right)i^{2}
Multiply complex numbers 8+4i and 3-2i like you multiply binomials.
8\times 3+8\times \left(-2i\right)+4i\times 3+4\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
24-16i+12i+8
Do the multiplications.
24+8+\left(-16+12\right)i
Combine the real and imaginary parts.
32-4i
Do the additions.
Re(8\times 3+8\times \left(-2i\right)+4i\times 3+4\left(-2\right)i^{2})
Multiply complex numbers 8+4i and 3-2i like you multiply binomials.
Re(8\times 3+8\times \left(-2i\right)+4i\times 3+4\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(24-16i+12i+8)
Do the multiplications in 8\times 3+8\times \left(-2i\right)+4i\times 3+4\left(-2\right)\left(-1\right).
Re(24+8+\left(-16+12\right)i)
Combine the real and imaginary parts in 24-16i+12i+8.
Re(32-4i)
Do the additions in 24+8+\left(-16+12\right)i.
32
The real part of 32-4i is 32.
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