2 ( 4 ( 1 + i ) - 3 ( 1 + i ) - 3 ( 2 ( 1 + i ) + 1 - i )
Evaluate
-16-4i
Real Part
-16
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2\left(4\times 1+4i-3\left(1+i\right)-3\left(2\left(1+i\right)+1-i\right)\right)
Multiply 4 times 1+i.
2\left(4+4i-3\left(1+i\right)-3\left(2\left(1+i\right)+1-i\right)\right)
Do the multiplications in 4\times 1+4i.
2\left(4+4i-\left(3\times 1+3i\right)-3\left(2\left(1+i\right)+1-i\right)\right)
Multiply 3 times 1+i.
2\left(4+4i-\left(3+3i\right)-3\left(2\left(1+i\right)+1-i\right)\right)
Do the multiplications in 3\times 1+3i.
2\left(4-3+\left(4-3\right)i-3\left(2\left(1+i\right)+1-i\right)\right)
Subtract 3+3i from 4+4i by subtracting corresponding real and imaginary parts.
2\left(1+i-3\left(2\left(1+i\right)+1-i\right)\right)
Subtract 3 from 4. Subtract 3 from 4.
2\left(1+i-3\left(2\times 1+2i+1-i\right)\right)
Multiply 2 times 1+i.
2\left(1+i-3\left(2+2i+1-i\right)\right)
Do the multiplications in 2\times 1+2i.
2\left(1+i-3\left(2+1+\left(2-1\right)i\right)\right)
Combine the real and imaginary parts in 2+2i+1-i.
2\left(1+i-3\left(3+i\right)\right)
Do the additions in 2+1+\left(2-1\right)i.
2\left(1+i-\left(3\times 3+3i\right)\right)
Multiply 3 times 3+i.
2\left(1+i-\left(9+3i\right)\right)
Do the multiplications in 3\times 3+3i.
2\left(1-9+\left(1-3\right)i\right)
Subtract 9+3i from 1+i by subtracting corresponding real and imaginary parts.
2\left(-8-2i\right)
Subtract 9 from 1. Subtract 3 from 1.
2\left(-8\right)+2\times \left(-2i\right)
Multiply 2 times -8-2i.
-16-4i
Do the multiplications.
Re(2\left(4\times 1+4i-3\left(1+i\right)-3\left(2\left(1+i\right)+1-i\right)\right))
Multiply 4 times 1+i.
Re(2\left(4+4i-3\left(1+i\right)-3\left(2\left(1+i\right)+1-i\right)\right))
Do the multiplications in 4\times 1+4i.
Re(2\left(4+4i-\left(3\times 1+3i\right)-3\left(2\left(1+i\right)+1-i\right)\right))
Multiply 3 times 1+i.
Re(2\left(4+4i-\left(3+3i\right)-3\left(2\left(1+i\right)+1-i\right)\right))
Do the multiplications in 3\times 1+3i.
Re(2\left(4-3+\left(4-3\right)i-3\left(2\left(1+i\right)+1-i\right)\right))
Subtract 3+3i from 4+4i by subtracting corresponding real and imaginary parts.
Re(2\left(1+i-3\left(2\left(1+i\right)+1-i\right)\right))
Subtract 3 from 4. Subtract 3 from 4.
Re(2\left(1+i-3\left(2\times 1+2i+1-i\right)\right))
Multiply 2 times 1+i.
Re(2\left(1+i-3\left(2+2i+1-i\right)\right))
Do the multiplications in 2\times 1+2i.
Re(2\left(1+i-3\left(2+1+\left(2-1\right)i\right)\right))
Combine the real and imaginary parts in 2+2i+1-i.
Re(2\left(1+i-3\left(3+i\right)\right))
Do the additions in 2+1+\left(2-1\right)i.
Re(2\left(1+i-\left(3\times 3+3i\right)\right))
Multiply 3 times 3+i.
Re(2\left(1+i-\left(9+3i\right)\right))
Do the multiplications in 3\times 3+3i.
Re(2\left(1-9+\left(1-3\right)i\right))
Subtract 9+3i from 1+i by subtracting corresponding real and imaginary parts.
Re(2\left(-8-2i\right))
Subtract 9 from 1. Subtract 3 from 1.
Re(2\left(-8\right)+2\times \left(-2i\right))
Multiply 2 times -8-2i.
Re(-16-4i)
Do the multiplications in 2\left(-8\right)+2\times \left(-2i\right).
-16
The real part of -16-4i is -16.
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Limits
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