Evaluate
12-76i
Real Part
12
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7\left(-4\right)+7\times \left(-8i\right)+5i\left(-4\right)+5\left(-8\right)i^{2}
Multiply complex numbers 7+5i and -4-8i like you multiply binomials.
7\left(-4\right)+7\times \left(-8i\right)+5i\left(-4\right)+5\left(-8\right)\left(-1\right)
By definition, i^{2} is -1.
-28-56i-20i+40
Do the multiplications.
-28+40+\left(-56-20\right)i
Combine the real and imaginary parts.
12-76i
Do the additions.
Re(7\left(-4\right)+7\times \left(-8i\right)+5i\left(-4\right)+5\left(-8\right)i^{2})
Multiply complex numbers 7+5i and -4-8i like you multiply binomials.
Re(7\left(-4\right)+7\times \left(-8i\right)+5i\left(-4\right)+5\left(-8\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-28-56i-20i+40)
Do the multiplications in 7\left(-4\right)+7\times \left(-8i\right)+5i\left(-4\right)+5\left(-8\right)\left(-1\right).
Re(-28+40+\left(-56-20\right)i)
Combine the real and imaginary parts in -28-56i-20i+40.
Re(12-76i)
Do the additions in -28+40+\left(-56-20\right)i.
12
The real part of 12-76i is 12.
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