Evaluate
31+17i
Real Part
31
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7\times 4+7\times \left(3i\right)-i\times 4-3i^{2}
Multiply complex numbers 7-i and 4+3i like you multiply binomials.
7\times 4+7\times \left(3i\right)-i\times 4-3\left(-1\right)
By definition, i^{2} is -1.
28+21i-4i+3
Do the multiplications.
28+3+\left(21-4\right)i
Combine the real and imaginary parts.
31+17i
Do the additions.
Re(7\times 4+7\times \left(3i\right)-i\times 4-3i^{2})
Multiply complex numbers 7-i and 4+3i like you multiply binomials.
Re(7\times 4+7\times \left(3i\right)-i\times 4-3\left(-1\right))
By definition, i^{2} is -1.
Re(28+21i-4i+3)
Do the multiplications in 7\times 4+7\times \left(3i\right)-i\times 4-3\left(-1\right).
Re(28+3+\left(21-4\right)i)
Combine the real and imaginary parts in 28+21i-4i+3.
Re(31+17i)
Do the additions in 28+3+\left(21-4\right)i.
31
The real part of 31+17i is 31.
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