Evaluate
-120-40i
Real Part
-120
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10\left(-8\right)+10\times \left(-8i\right)-5i\left(-8\right)-5\left(-8\right)i^{2}
Multiply complex numbers 10-5i and -8-8i like you multiply binomials.
10\left(-8\right)+10\times \left(-8i\right)-5i\left(-8\right)-5\left(-8\right)\left(-1\right)
By definition, i^{2} is -1.
-80-80i+40i-40
Do the multiplications.
-80-40+\left(-80+40\right)i
Combine the real and imaginary parts.
-120-40i
Do the additions.
Re(10\left(-8\right)+10\times \left(-8i\right)-5i\left(-8\right)-5\left(-8\right)i^{2})
Multiply complex numbers 10-5i and -8-8i like you multiply binomials.
Re(10\left(-8\right)+10\times \left(-8i\right)-5i\left(-8\right)-5\left(-8\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-80-80i+40i-40)
Do the multiplications in 10\left(-8\right)+10\times \left(-8i\right)-5i\left(-8\right)-5\left(-8\right)\left(-1\right).
Re(-80-40+\left(-80+40\right)i)
Combine the real and imaginary parts in -80-80i+40i-40.
Re(-120-40i)
Do the additions in -80-40+\left(-80+40\right)i.
-120
The real part of -120-40i is -120.
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