Evaluate
10
Real Part
10
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3\times 3+3i-i\times 3-i^{2}
Multiply complex numbers 3-i and 3+i like you multiply binomials.
3\times 3+3i-i\times 3-\left(-1\right)
By definition, i^{2} is -1.
9+3i-3i+1
Do the multiplications.
9+1+\left(3-3\right)i
Combine the real and imaginary parts.
10
Do the additions.
Re(3\times 3+3i-i\times 3-i^{2})
Multiply complex numbers 3-i and 3+i like you multiply binomials.
Re(3\times 3+3i-i\times 3-\left(-1\right))
By definition, i^{2} is -1.
Re(9+3i-3i+1)
Do the multiplications in 3\times 3+3i-i\times 3-\left(-1\right).
Re(9+1+\left(3-3\right)i)
Combine the real and imaginary parts in 9+3i-3i+1.
Re(10)
Do the additions in 9+1+\left(3-3\right)i.
10
The real part of 10 is 10.
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