Evaluate
40+40i
Real Part
40
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2\times 8+2\times \left(-4i\right)+6i\times 8+6\left(-4\right)i^{2}
Multiply complex numbers 2+6i and 8-4i like you multiply binomials.
2\times 8+2\times \left(-4i\right)+6i\times 8+6\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
16-8i+48i+24
Do the multiplications.
16+24+\left(-8+48\right)i
Combine the real and imaginary parts.
40+40i
Do the additions.
Re(2\times 8+2\times \left(-4i\right)+6i\times 8+6\left(-4\right)i^{2})
Multiply complex numbers 2+6i and 8-4i like you multiply binomials.
Re(2\times 8+2\times \left(-4i\right)+6i\times 8+6\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(16-8i+48i+24)
Do the multiplications in 2\times 8+2\times \left(-4i\right)+6i\times 8+6\left(-4\right)\left(-1\right).
Re(16+24+\left(-8+48\right)i)
Combine the real and imaginary parts in 16-8i+48i+24.
Re(40+40i)
Do the additions in 16+24+\left(-8+48\right)i.
40
The real part of 40+40i is 40.
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