Evaluate
41-59i
Real Part
41
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7\times 8+7\times \left(-5i\right)-3i\times 8-3\left(-5\right)i^{2}
Multiply complex numbers 7-3i and 8-5i like you multiply binomials.
7\times 8+7\times \left(-5i\right)-3i\times 8-3\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
56-35i-24i-15
Do the multiplications.
56-15+\left(-35-24\right)i
Combine the real and imaginary parts.
41-59i
Do the additions.
Re(7\times 8+7\times \left(-5i\right)-3i\times 8-3\left(-5\right)i^{2})
Multiply complex numbers 7-3i and 8-5i like you multiply binomials.
Re(7\times 8+7\times \left(-5i\right)-3i\times 8-3\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(56-35i-24i-15)
Do the multiplications in 7\times 8+7\times \left(-5i\right)-3i\times 8-3\left(-5\right)\left(-1\right).
Re(56-15+\left(-35-24\right)i)
Combine the real and imaginary parts in 56-35i-24i-15.
Re(41-59i)
Do the additions in 56-15+\left(-35-24\right)i.
41
The real part of 41-59i is 41.
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