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