Evaluate
14+3i
Real Part
14
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2+3i\times 1+3\left(-4\right)i^{2}
Multiply 3i times 1-4i.
2+3i\times 1+3\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
2+\left(12+3i\right)
Do the multiplications in 3i\times 1+3\left(-4\right)\left(-1\right). Reorder the terms.
2+12+3i
Combine the real and imaginary parts.
14+3i
Add 2 to 12.
Re(2+3i\times 1+3\left(-4\right)i^{2})
Multiply 3i times 1-4i.
Re(2+3i\times 1+3\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(2+\left(12+3i\right))
Do the multiplications in 3i\times 1+3\left(-4\right)\left(-1\right). Reorder the terms.
Re(2+12+3i)
Combine the real and imaginary parts in 2+12+3i.
Re(14+3i)
Add 2 to 12.
14
The real part of 14+3i is 14.
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