Evaluate
31-14i
Real Part
31
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3\times 5+3\times \left(-8i\right)+2i\times 5+2\left(-8\right)i^{2}
Multiply complex numbers 3+2i and 5-8i like you multiply binomials.
3\times 5+3\times \left(-8i\right)+2i\times 5+2\left(-8\right)\left(-1\right)
By definition, i^{2} is -1.
15-24i+10i+16
Do the multiplications.
15+16+\left(-24+10\right)i
Combine the real and imaginary parts.
31-14i
Do the additions.
Re(3\times 5+3\times \left(-8i\right)+2i\times 5+2\left(-8\right)i^{2})
Multiply complex numbers 3+2i and 5-8i like you multiply binomials.
Re(3\times 5+3\times \left(-8i\right)+2i\times 5+2\left(-8\right)\left(-1\right))
By definition, i^{2} is -1.
Re(15-24i+10i+16)
Do the multiplications in 3\times 5+3\times \left(-8i\right)+2i\times 5+2\left(-8\right)\left(-1\right).
Re(15+16+\left(-24+10\right)i)
Combine the real and imaginary parts in 15-24i+10i+16.
Re(31-14i)
Do the additions in 15+16+\left(-24+10\right)i.
31
The real part of 31-14i is 31.
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