Evaluate
14-8i
Real Part
14
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4\times 2+4\times \left(-3i\right)+2i\times 2+2\left(-3\right)i^{2}
Multiply complex numbers 4+2i and 2-3i like you multiply binomials.
4\times 2+4\times \left(-3i\right)+2i\times 2+2\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
8-12i+4i+6
Do the multiplications.
8+6+\left(-12+4\right)i
Combine the real and imaginary parts.
14-8i
Do the additions.
Re(4\times 2+4\times \left(-3i\right)+2i\times 2+2\left(-3\right)i^{2})
Multiply complex numbers 4+2i and 2-3i like you multiply binomials.
Re(4\times 2+4\times \left(-3i\right)+2i\times 2+2\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(8-12i+4i+6)
Do the multiplications in 4\times 2+4\times \left(-3i\right)+2i\times 2+2\left(-3\right)\left(-1\right).
Re(8+6+\left(-12+4\right)i)
Combine the real and imaginary parts in 8-12i+4i+6.
Re(14-8i)
Do the additions in 8+6+\left(-12+4\right)i.
14
The real part of 14-8i is 14.
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