Evaluate
14+40i
Real Part
14
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8\times 1+8\times \left(2i\right)+3i\left(8-2i\right)
Multiply 8 times 1+2i.
8+16i+3i\left(8-2i\right)
Do the multiplications in 8\times 1+8\times \left(2i\right).
8+16i+3i\times 8+3\left(-2\right)i^{2}
Multiply 3i times 8-2i.
8+16i+3i\times 8+3\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
8+16i+\left(6+24i\right)
Do the multiplications in 3i\times 8+3\left(-2\right)\left(-1\right). Reorder the terms.
8+6+\left(16+24\right)i
Combine the real and imaginary parts.
14+40i
Do the additions.
Re(8\times 1+8\times \left(2i\right)+3i\left(8-2i\right))
Multiply 8 times 1+2i.
Re(8+16i+3i\left(8-2i\right))
Do the multiplications in 8\times 1+8\times \left(2i\right).
Re(8+16i+3i\times 8+3\left(-2\right)i^{2})
Multiply 3i times 8-2i.
Re(8+16i+3i\times 8+3\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(8+16i+\left(6+24i\right))
Do the multiplications in 3i\times 8+3\left(-2\right)\left(-1\right). Reorder the terms.
Re(8+6+\left(16+24\right)i)
Combine the real and imaginary parts in 8+16i+6+24i.
Re(14+40i)
Do the additions in 8+6+\left(16+24\right)i.
14
The real part of 14+40i is 14.
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