Evaluate
33+10i
Real Part
33
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-2\left(-4\right)-2\times \left(5i\right)-5i\left(-4\right)-5\times 5i^{2}
Multiply complex numbers -2-5i and -4+5i like you multiply binomials.
-2\left(-4\right)-2\times \left(5i\right)-5i\left(-4\right)-5\times 5\left(-1\right)
By definition, i^{2} is -1.
8-10i+20i+25
Do the multiplications.
8+25+\left(-10+20\right)i
Combine the real and imaginary parts.
33+10i
Do the additions.
Re(-2\left(-4\right)-2\times \left(5i\right)-5i\left(-4\right)-5\times 5i^{2})
Multiply complex numbers -2-5i and -4+5i like you multiply binomials.
Re(-2\left(-4\right)-2\times \left(5i\right)-5i\left(-4\right)-5\times 5\left(-1\right))
By definition, i^{2} is -1.
Re(8-10i+20i+25)
Do the multiplications in -2\left(-4\right)-2\times \left(5i\right)-5i\left(-4\right)-5\times 5\left(-1\right).
Re(8+25+\left(-10+20\right)i)
Combine the real and imaginary parts in 8-10i+20i+25.
Re(33+10i)
Do the additions in 8+25+\left(-10+20\right)i.
33
The real part of 33+10i is 33.
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Limits
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