Evaluate
16+2i
Real Part
16
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3\times 5+3\left(-i\right)+5i-i^{2}
Multiply complex numbers 3+i and 5-i like you multiply binomials.
3\times 5+3\left(-i\right)+5i-\left(-1\right)
By definition, i^{2} is -1.
15-3i+5i+1
Do the multiplications.
15+1+\left(-3+5\right)i
Combine the real and imaginary parts.
16+2i
Do the additions.
Re(3\times 5+3\left(-i\right)+5i-i^{2})
Multiply complex numbers 3+i and 5-i like you multiply binomials.
Re(3\times 5+3\left(-i\right)+5i-\left(-1\right))
By definition, i^{2} is -1.
Re(15-3i+5i+1)
Do the multiplications in 3\times 5+3\left(-i\right)+5i-\left(-1\right).
Re(15+1+\left(-3+5\right)i)
Combine the real and imaginary parts in 15-3i+5i+1.
Re(16+2i)
Do the additions in 15+1+\left(-3+5\right)i.
16
The real part of 16+2i is 16.
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