Evaluate
20+12i
Real Part
20
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2\times 2+2\times \left(-2i\right)+8i\times 2+8\left(-2\right)i^{2}
Multiply complex numbers 2+8i and 2-2i like you multiply binomials.
2\times 2+2\times \left(-2i\right)+8i\times 2+8\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
4-4i+16i+16
Do the multiplications.
4+16+\left(-4+16\right)i
Combine the real and imaginary parts.
20+12i
Do the additions.
Re(2\times 2+2\times \left(-2i\right)+8i\times 2+8\left(-2\right)i^{2})
Multiply complex numbers 2+8i and 2-2i like you multiply binomials.
Re(2\times 2+2\times \left(-2i\right)+8i\times 2+8\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(4-4i+16i+16)
Do the multiplications in 2\times 2+2\times \left(-2i\right)+8i\times 2+8\left(-2\right)\left(-1\right).
Re(4+16+\left(-4+16\right)i)
Combine the real and imaginary parts in 4-4i+16i+16.
Re(20+12i)
Do the additions in 4+16+\left(-4+16\right)i.
20
The real part of 20+12i is 20.
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