Evaluate
-6-11i
Real Part
-6
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2i\times 7+2\times 3i^{2}+5\times \left(-5i\right)
Multiply 2i times 7+3i.
2i\times 7+2\times 3\left(-1\right)+5\times \left(-5i\right)
By definition, i^{2} is -1.
-6+14i+5\times \left(-5i\right)
Do the multiplications in 2i\times 7+2\times 3\left(-1\right). Reorder the terms.
-6+14i-25i
Multiply 5 and -5i to get -25i.
-6+\left(14-25\right)i
Combine the real and imaginary parts.
-6-11i
Add 14 to -25.
Re(2i\times 7+2\times 3i^{2}+5\times \left(-5i\right))
Multiply 2i times 7+3i.
Re(2i\times 7+2\times 3\left(-1\right)+5\times \left(-5i\right))
By definition, i^{2} is -1.
Re(-6+14i+5\times \left(-5i\right))
Do the multiplications in 2i\times 7+2\times 3\left(-1\right). Reorder the terms.
Re(-6+14i-25i)
Multiply 5 and -5i to get -25i.
Re(-6+\left(14-25\right)i)
Combine the real and imaginary parts in -6+14i-25i.
Re(-6-11i)
Add 14 to -25.
-6
The real part of -6-11i is -6.
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