Evaluate
10+2i
Real Part
10
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12+0-2i\left(-1-i\right)
Multiply 0 and 7i to get 0.
12-2i\left(-1-i\right)
Add 12 and 0 to get 12.
12-\left(2i\left(-1\right)+2\left(-1\right)i^{2}\right)
Multiply 2i times -1-i.
12-\left(2i\left(-1\right)+2\left(-1\right)\left(-1\right)\right)
By definition, i^{2} is -1.
12-\left(2-2i\right)
Do the multiplications in 2i\left(-1\right)+2\left(-1\right)\left(-1\right). Reorder the terms.
12-2-2i
Subtract 2-2i from 12 by subtracting corresponding real and imaginary parts.
10+2i
Subtract 2 from 12.
Re(12+0-2i\left(-1-i\right))
Multiply 0 and 7i to get 0.
Re(12-2i\left(-1-i\right))
Add 12 and 0 to get 12.
Re(12-\left(2i\left(-1\right)+2\left(-1\right)i^{2}\right))
Multiply 2i times -1-i.
Re(12-\left(2i\left(-1\right)+2\left(-1\right)\left(-1\right)\right))
By definition, i^{2} is -1.
Re(12-\left(2-2i\right))
Do the multiplications in 2i\left(-1\right)+2\left(-1\right)\left(-1\right). Reorder the terms.
Re(12-2-2i)
Subtract 2-2i from 12 by subtracting corresponding real and imaginary parts.
Re(10+2i)
Subtract 2 from 12.
10
The real part of 10+2i is 10.
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Limits
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