Evaluate
2-16i
Real Part
2
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1\left(-3\right)+1\left(-i\right)+5i\left(-3\right)+5\left(-1\right)i^{2}
Multiply complex numbers 1+5i and -3-i like you multiply binomials.
1\left(-3\right)+1\left(-i\right)+5i\left(-3\right)+5\left(-1\right)\left(-1\right)
By definition, i^{2} is -1.
-3-i-15i+5
Do the multiplications.
-3+5+\left(-1-15\right)i
Combine the real and imaginary parts.
2-16i
Do the additions.
Re(1\left(-3\right)+1\left(-i\right)+5i\left(-3\right)+5\left(-1\right)i^{2})
Multiply complex numbers 1+5i and -3-i like you multiply binomials.
Re(1\left(-3\right)+1\left(-i\right)+5i\left(-3\right)+5\left(-1\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-3-i-15i+5)
Do the multiplications in 1\left(-3\right)+1\left(-i\right)+5i\left(-3\right)+5\left(-1\right)\left(-1\right).
Re(-3+5+\left(-1-15\right)i)
Combine the real and imaginary parts in -3-i-15i+5.
Re(2-16i)
Do the additions in -3+5+\left(-1-15\right)i.
2
The real part of 2-16i is 2.
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