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3\times 6+3\times \left(2i\right)-i\times 6-2i^{2}
Multiply complex numbers 3-i and 6+2i like you multiply binomials.
3\times 6+3\times \left(2i\right)-i\times 6-2\left(-1\right)
By definition, i^{2} is -1.
18+6i-6i+2
Do the multiplications.
18+2+\left(6-6\right)i
Combine the real and imaginary parts.
20
Do the additions.
Re(3\times 6+3\times \left(2i\right)-i\times 6-2i^{2})
Multiply complex numbers 3-i and 6+2i like you multiply binomials.
Re(3\times 6+3\times \left(2i\right)-i\times 6-2\left(-1\right))
By definition, i^{2} is -1.
Re(18+6i-6i+2)
Do the multiplications in 3\times 6+3\times \left(2i\right)-i\times 6-2\left(-1\right).
Re(18+2+\left(6-6\right)i)
Combine the real and imaginary parts in 18+6i-6i+2.
Re(20)
Do the additions in 18+2+\left(6-6\right)i.
20
The real part of 20 is 20.