Evaluate
11-8i
Real Part
11
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3-2i\left(4+\left(3+1\right)i\right)
Combine the real and imaginary parts in numbers 4+3i and i.
3-2i\left(4+4i\right)
Add 3 to 1.
3-\left(2i\times 4+2\times 4i^{2}\right)
Multiply 2i times 4+4i.
3-\left(2i\times 4+2\times 4\left(-1\right)\right)
By definition, i^{2} is -1.
3-\left(-8+8i\right)
Do the multiplications in 2i\times 4+2\times 4\left(-1\right). Reorder the terms.
3-\left(-8\right)+8i
Subtract -8+8i from 3 by subtracting corresponding real and imaginary parts.
11-8i
Subtract -8 from 3.
Re(3-2i\left(4+\left(3+1\right)i\right))
Combine the real and imaginary parts in numbers 4+3i and i.
Re(3-2i\left(4+4i\right))
Add 3 to 1.
Re(3-\left(2i\times 4+2\times 4i^{2}\right))
Multiply 2i times 4+4i.
Re(3-\left(2i\times 4+2\times 4\left(-1\right)\right))
By definition, i^{2} is -1.
Re(3-\left(-8+8i\right))
Do the multiplications in 2i\times 4+2\times 4\left(-1\right). Reorder the terms.
Re(3-\left(-8\right)+8i)
Subtract -8+8i from 3 by subtracting corresponding real and imaginary parts.
Re(11-8i)
Subtract -8 from 3.
11
The real part of 11-8i is 11.
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