Evaluate
-7-19i
Real Part
-7
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2i\left(-8\right)+2\left(-1\right)i^{2}+3\left(-3-i\right)
Multiply 2i times -8-i.
2i\left(-8\right)+2\left(-1\right)\left(-1\right)+3\left(-3-i\right)
By definition, i^{2} is -1.
2-16i+3\left(-3-i\right)
Do the multiplications in 2i\left(-8\right)+2\left(-1\right)\left(-1\right). Reorder the terms.
2-16i+3\left(-3\right)+3\left(-i\right)
Multiply 3 times -3-i.
2-16i+\left(-9-3i\right)
Do the multiplications in 3\left(-3\right)+3\left(-i\right).
2-9+\left(-16-3\right)i
Combine the real and imaginary parts.
-7-19i
Do the additions.
Re(2i\left(-8\right)+2\left(-1\right)i^{2}+3\left(-3-i\right))
Multiply 2i times -8-i.
Re(2i\left(-8\right)+2\left(-1\right)\left(-1\right)+3\left(-3-i\right))
By definition, i^{2} is -1.
Re(2-16i+3\left(-3-i\right))
Do the multiplications in 2i\left(-8\right)+2\left(-1\right)\left(-1\right). Reorder the terms.
Re(2-16i+3\left(-3\right)+3\left(-i\right))
Multiply 3 times -3-i.
Re(2-16i+\left(-9-3i\right))
Do the multiplications in 3\left(-3\right)+3\left(-i\right).
Re(2-9+\left(-16-3\right)i)
Combine the real and imaginary parts in 2-16i-9-3i.
Re(-7-19i)
Do the additions in 2-9+\left(-16-3\right)i.
-7
The real part of -7-19i is -7.
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