Evaluate
10+28i
Real Part
10
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1\left(-5\right)+1\times \left(3i\right)-5i\left(-5\right)-5\times 3i^{2}
Multiply complex numbers 1-5i and -5+3i like you multiply binomials.
1\left(-5\right)+1\times \left(3i\right)-5i\left(-5\right)-5\times 3\left(-1\right)
By definition, i^{2} is -1.
-5+3i+25i+15
Do the multiplications.
-5+15+\left(3+25\right)i
Combine the real and imaginary parts.
10+28i
Do the additions.
Re(1\left(-5\right)+1\times \left(3i\right)-5i\left(-5\right)-5\times 3i^{2})
Multiply complex numbers 1-5i and -5+3i like you multiply binomials.
Re(1\left(-5\right)+1\times \left(3i\right)-5i\left(-5\right)-5\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(-5+3i+25i+15)
Do the multiplications in 1\left(-5\right)+1\times \left(3i\right)-5i\left(-5\right)-5\times 3\left(-1\right).
Re(-5+15+\left(3+25\right)i)
Combine the real and imaginary parts in -5+3i+25i+15.
Re(10+28i)
Do the additions in -5+15+\left(3+25\right)i.
10
The real part of 10+28i is 10.
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